Integrative optics system, device, and method

ABSTRACT

A laser is used to emit a diverging laser flash configured to illuminate a detection zone. A pseudoimaging optical receiver system is used to detect reflections from objects in the detection zone. The receiver system includes a time-gated photodetector array that is used to record signatures in a voxel array. A voxel processing module receives the voxel array and detects a reference clutter signal within the array. Potential targets are then detected according to target signals in relation to the reference clutter signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of application Ser. No. 13/913,090,filed on Jun. 7, 2013, which has been assigned U.S. Pat. No. 9,689,987,issuing on Jun. 27, 2017, which claims the benefit of U.S. ProvisionalApplication No. 61/659,348, filed Jun. 13, 2012; U.S. ProvisionalApplication No. 61/675,256, filed Jul. 24, 2012; and U.S. ProvisionalApplication No. 61/718,154, filed Oct. 24, 2012, which are herebyincorporated herein by reference in their entireties.

STATEMENT OF GOVERNMENT RIGHTS

One or more inventions described herein are partially supported by thefollowing contracts for the Department of Navy under the SBIR program:M67854-10-C-6531, N00024-06-C-4121, N00014-09-C-0456, andN00014-05-C-0423. The Government may have partial rights in suchinventions.

TECHNICAL FIELD

The present invention relates generally to object detection systems, andmore particularly, some embodiments relate to systems and methods forlong distance optical detection.

DESCRIPTION OF THE RELATED ART

Clutter can cause serious performance issues in object detectionsystems, such as radar, LIDAR, sonar, and imaging systems. For example,in littoral environments, wave clutter can severely impede the abilityof a radar system to detect objects such as periscopes.

BRIEF SUMMARY OF EMBODIMENTS OF THE INVENTION

Optical detection systems are provided for detecting objects in thepresence of clutter and discriminating between target objects andclutter. In some embodiments, the system is configured for detection ofhigh brightness objects and light sources—for example, non-Lambertianreflectors, such as retroreflectors.

In some embodiments, the system mitigates clutter in the scene byreducing false positives or increasing positive predictive values (PPV).Various signals may be used for target discrimination. For example,clutter signal patterns associated with known target types may bedetected along with potential target signals. Additionally, specifictarget signals may be detected. For example, multiple retroreflectionsfrom a single ocular body may be detected, and the character of thesemultiple retrorefelections may be used for target discrimination.

In various embodiments, an eye-safe laser is used to emit a diverginglaser flash configured to illuminate a detection zone. A pseudoimagingoptical receiver system is used to detect reflections from objects inthe detection zone. The receiver system includes a time-gatedphotodetector array that is used to record signatures in a voxel array.A voxel processing module receives the voxel array and detects areference clutter signal within the array. Potential targets are thendetected according to target signals in relation to the referenceclutter signal.

Further embodiments of the invention use a temporal sequence ofvoxel-arrays from the same detection zone to implement voxel changedetection. Potential target may be detected according to varioustemporal voxel signatures. More generally, the potential target maydetected space/time voxel patterns manifested by voxel coherence.

Other features and aspects of the invention will become apparent fromthe following detailed description, taken in conjunction with theaccompanying drawings, which illustrate, by way of example, the featuresin accordance with embodiments of the invention. The summary is notintended to limit the scope of the invention, which is defined solely bythe claims attached hereto.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention, in accordance with one or more variousembodiments, is described in detail with reference to the followingfigures. The drawings are provided for purposes of illustration only andmerely depict typical or example embodiments of the invention. Thesedrawings are provided to facilitate the reader's understanding of theinvention and shall not be considered limiting of the breadth, scope, orapplicability of the invention. It should be noted that for clarity andease of illustration these drawings are not necessarily made to scale.

Some of the figures included herein illustrate various embodiments ofthe invention from different viewing angles. Although the accompanyingdescriptive text may refer to such views as “top,” “bottom” or “side”views, such references are merely descriptive and do not imply orrequire that the invention be implemented or used in a particularspatial orientation unless explicitly stated otherwise.

FIG. 1 illustrates an example system module.

FIG. 2 illustrates an example dual-module system.

FIG. 3 illustrates an example system deployment.

FIGS. 4A-B illustrate a top down view of the field of view and detectionzone of an example system.

FIG. 5 illustrates an example laser source.

FIG. 6 illustrates an example laser delivery system.

FIG. 7 illustrates an example beam expander.

FIG. 8 illustrates an example beam reshuffler.

FIG. 9 illustrates an example of system geometry during operation.

FIG. 10 illustrates an example fiber optic laser delivery component.

FIG. 11A illustrates an example laser reception system.

FIG. 11B illustrates an example laser reception system.

FIG. 110 illustrates an example laser reception system.

FIG. 11D illustrates an example laser reception system.

FIG. 12A illustrates an example sensor layout.

FIG. 12B illustrates an example sensor layout.

FIG. 13A illustrates an example reception optic.

FIG. 13B illustrates an example reception optic.

FIG. 130 illustrates an example reception optic.

FIG. 13D illustrates an example reception optic.

FIG. 14A illustrates a tapered fiber optic for laser receivers.

FIG. 14B illustrates a tapered fiber optic for laser receivers.

FIG. 15 illustrates an example of system operation during scanning.

FIG. 16 illustrates an example of target detection.

FIG. 17A illustrates an example step of target detection methods.

FIG. 17B illustrates an example step of target detection methods.

FIG. 18A illustrates an example step of target detection methods.

FIG. 18B illustrates an example step of target detection methods.

FIG. 180 illustrates an example step of target detection methods.

FIG. 19 illustrates voxel coherence in a vertical line of voxels.

FIG. 20 illustrates an example of horizontal voxel coherency.

FIG. 21A illustrates space-time correlation between voxels.

FIG. 21B illustrates space-time correlation between voxels.

FIG. 210 illustrates space-time correlation between voxels.

FIG. 21D illustrates space-time correlation between voxels.

FIG. 22 illustrates a inference method of target detectiondiscrimination for periscopes.

FIG. 23 illustrates an additional method of target detectiondiscrimination for periscopes.

FIG. 24 illustrates an example of rigid foxel group movement.

FIG. 25 illustrates a second example of rigid foxel group movement.

FIG. 26 illustrates an example of non-rigid foxel group movement.

FIG. 27 illustrates an example of velocity flow mapping.

FIG. 28 illustrates an example system implementation for trip-wiredetection.

FIG. 29A illustrates an example system implementation for fingerprintdetection.

FIG. 29B illustrates an example system implementation for fingerprintdetection.

FIG. 30A illustrates an example of pulse partition sampling.

FIG. 30B illustrates an example of pulse partition sampling.

FIG. 31A illustrates detection of pulse reflection deformation byvarious surfaces.

FIG. 31B illustrates detection of pulse reflection deformation byvarious surfaces.

FIG. 31C illustrates detection of pulse reflection deformation byvarious surfaces.

FIG. 31D illustrates detection of pulse reflection deformation byvarious surfaces.

FIG. 31E illustrates detection of pulse reflection deformation byvarious surfaces.

FIG. 31F illustrates detection of pulse reflection deformation byvarious surfaces.

FIG. 32 illustrates an example computing module that may be used inimplementing various features of embodiments of the invention.

The figures are not intended to be exhaustive or to limit the inventionto the precise form disclosed. It should be understood that theinvention can be practiced with modification and alteration, and thatthe invention be limited only by the claims and the equivalents thereof.

DETAILED DESCRIPTION

As used herein the term “sensor” or “pixel” refers generally to anelement of a sensor array. For example, the term sensor or pixel mayrefer to an individual photodetector of a photodetector array (“PDA”).In other cases, as indicated by context, the term “sensor” may refer toan entire sensor or pixel array.

FIG. 1 illustrates an exemplary integrative optics system. The systemcomprises a housing 100 mounted on a stabilized platform 101. One ormore detection modules 105 are disposed within the housing. Eachdetection module 105 comprises a laser emitter 103 and an opticalreceiver 102. The module has a total field of view (FOV) 104. The totalfield of view is achieved by emitting flashes (or facets) that encompassa sub-range of the total field of view. The emitter 103 and the receiver102 scan the total field of view using a plurality of facets atdifferent angles. For example, to cover a 180° field of view, thehousing may comprise 5 modules 105, each having a 40° field of view(with some overlap between fields of view). Each module 105 may emitflashes along about 100 facet angles, each flash having a 0.4° field ofview. In another embodiment, the modules 105 scan to cover a pluralityof views. For example, rather than 5 different modules 105 to cover a180° field of view, a single module 105 may move to 5 differentpositions. For example, the stabilizing platform 101 may rotate thehousing 100 to the different positions. In some embodiments, thestabilizing platform 101 rotates the housing 100 in a staccato fashion,stopping for each flash and return signal. In other embodiments, thestabilizing platform 101 smoothly rotates, and transforms are performedon the data to compensate for the rotation.

FIG. 2 illustrates a second exemplary integrative optics system. In thissystem, multiple housings 207, 206 may house emitters and receivers toprovide additional fields of view 203, 204. In this particularimplementation, the system 201 is mounted on a semi-platform 205 of aships mast 202. In other embodiments, the system 201 may be mounted atother locations. For example, on a stationary tower (for example, onshore) or on an aircraft (for example, a helicopter).

FIG. 3 illustrates the system mounted on a marine platform. The FOV 307of a detection module of the system 201 comprises a plurality of facets302, 303, 304, 305. Each module may operate in parallel or serially withother modules to provide the full system FOV. Each facet FOV 302, 303,304, 305 is provided by a laser flash illuminating a detection volume ata distance from the laser light emitter. In some embodiments, thedetection volume is at least 3 km from the laser light emitter. Infurther embodiments, the laser is eye-safe, having a wavelength greaterthan 1.3 μm. In other embodiments, the laser has a wavelength greaterthan 1.5 μm. In still further embodiment, the laser is not eye-safe (forexample, the laser may have a wavelength of 1 μm). In such embodiments,a baffle or other shield may be disposed between the system andoperating personnel.

FIGS. 4A and 4B illustrate a top down view of the FOV and detection zoneof an embodiment. The system 400 has a FOV 401 and is comprises of aplurality of modules. Each module has a FOV 402, which when combinedprovide the entire FOV 401. Each module has an inner detection radius403 and an outer detection radius 406, to provide a detection zone 404.In some embodiments, the detection zone 404 is between an inner radius403 between 3 and 10 km and outer radius 406 between 10 and 30 km. Forexample, in a particular embodiment, the detection zone 404 is between 5km and 15 km. For single facet, its FOV=0.36°, for example, orFOV=0.00628, in radians. This is, for range of R=10 km, equivalent tohorizontal range of: 10⁴ m×0.00628=62.8 m, per single facet.

In still further embodiments, the emitter 103 is optomechanicallyadjustable to adjust the size or range of the detection zone. Eachmodule's FOV 402 is provided by the laser flashes 405 that illuminate adetection volume comprising a portion of the detection zone. The numberof flashes 405 may vary in different implementations based on factorssuch as module FOV size, desired operational frequency, available laserpower, available detection power, visibility, and other system orenvironmental factors. In one embodiment, for a detection zone between 5km and 15 km, with each flash illuminating about 100 m at the 15 kmradius, each flash has a horizontal FOV of 0.38° and a vertical FOV of0.37°.

Returning to FIG. 3, in the illustrated embodiment, the laser istransported to the emitter in the system head 201 from a laser sourceproximal to the mast base 301. FIG. 5 illustrates a cross section of asystem having a laser source 500 proximal to the base 301 of a mast 202.The laser source 500 emits a pulsed laser beam 501 into laser path 502.The pulsed laser beam 501 as sufficient peak power to illuminate thedetection volume sufficiently for return pulses to be detected by thedetector. In one embodiment, the peak laser power P₀ is greater than atleast 1 MW. In a particular embodiment, the laser pulse peak power is6.67×10⁶ W.

As an example, the following formula relating pulse energy, E_(O), andrepetition frequency, n, into equivalent continuous watt (CW) power, Pmay be applied:P=E _(O) ·n _(O)  (1)where n_(O) is nominal repetition frequency:n _(O)=100 Hz  (2)Therefore:

$\begin{matrix}{P_{o} = {\frac{E_{o}}{\tau_{L}} = \frac{\overset{\_}{P}}{n_{o}\tau_{L}}}} & (3)\end{matrix}$As an example, assume P=10 W, and n_(O)=100 Hz, then, E_(O)=P/n_(o)=10W/100 Hz=100 mJ, and for pulse length, t_(L)=10 nsec, P_(O)=100 mJ/10nsec=0.1 J/10⁻⁸ sec=10 MW.

In some embodiments, the laser path 502 may be free space, a waveguide,or an optical fiber. As discussed above, in some embodiments, the laserhas a peak power greater than 1 MW. Optical fibers have a laser damagethreshold which defines the maximum optical intensity in W/cm² that canbe transmitted in the fiber. In particular embodiments, the laser path502 comprises a multi-mode fiber with a core diameter of around 300 μm.

In one embodiment, the laser damage threshold is about:I _(O)=10 GW/cm²=10¹⁰ W/cm²  (4)Then, minimum fiber core diameter, (d_(F)) min, is

$\begin{matrix}{{\left( d_{F} \right)\min} = \sqrt{\frac{4P_{o}}{\pi\; I_{o}}}} & (5)\end{matrix}$where P_(O) is laser beam nominal power. Assuming, as before,P_(O)=6.67.10⁶ W, we obtain(d _(F))min=290 μm  (6), which is a multimode fiber. For a typical multi-mode fiber thenumerical aperture is N_(A)=0.4. From this, its etendue is: (2)(290 μm)(0.4)=232 μm, which is much larger than a laser's single-mode Gaussianbeam etendue, ε_(L), in the form:

$\begin{matrix}{ɛ_{L} = {{4\;\theta\;{w_{o}\left( \frac{\lambda}{\pi\; w_{o}} \right)}} = {\left. \frac{4\lambda}{\pi} \right.\sim\lambda}}} & (7)\end{matrix}$i.e., about 1.6 μm

In other embodiments, the laser beam path comprises a single modeoptics. In these embodiments, the laser beam may comprise a Gaussianbeam with divergence, 2θ, and beam waist, 2w_(O). For 2θ=Δϕ=0.38°,w_(O)=(1.6) (32) (10⁻⁴)/(0.033), =0.155 mm, and 2 w_(O)=310 μm>290 μm.The relation between the beam waist 2 w_(O) and divergence angle, 2θ indegrees, is summarized in Table 2.

TABLE 2 Relation between Gaussian Beam Waist, 2 w₀, and its divergence,2θ, for λ = 1.6 μm 2θ 1° 0.3° 0.1° 0.05° 0.03° 0.01° θ [Rad] 0.00870.0026 0.00087 0.0004 0.00026 0.000087 2 w_(o) [mm] 0.112 0.192 0.591.28 1.97 5.89

The emitter housing 503 comprises a beam coupler that couples the laserpath 502 to the laser emitter 504 and that conditions the beam 501 to beemitted 505. FIG. 6 illustrates the beam coupler 601 of the laserhousing coupled to the optical fiber laser path 502. The coupler 601conditions the beam by expanding the beam to obtain a desired beamprofile.

FIG. 7 illustrates one embodiment of the coupler 601. Here, the coupler601 comprises an entrance interface 702 in contact or coupled to an exitsurface of the fiber 502. The expanded beam fiber coupler 601 comprisesa material that has a similar refractive index, n₂, as the refractiveindex, n₁, of the fiber's 502 core. In some embodiments, the beamcoupler 601 is made of the same material as the fiber's 502 core. Instill further embodiments, the beam coupler 601 and fiber 502 core is acontinuous volume of material. The similarity of refractive indexesbetween the fiber 502 core and the beam coupler 601 reduces Fresnelreflection losses at the interface 702.

The coupler 601 has a profile 707 configured to provide a desiredintensity distribution 708 at the coupler exit 709. The desiredintensity distribution 708 may be symmetrical or asymmetrical.Symmetrical intensity distributions 708 may include circularlysymmetrical distributions, where intensity, I, is a function of radius,r. The intensity distribution 708 arises from total internal reflection(TIR) 705 of rays 704 within the beam coupler 601. In some embodiments,the intensity distribution 708 is Gaussian. In other embodiments, theintensity distribution 708 follows some other bell-shaped curve.

In some embodiments, the coupler exit 709 is optically coupled to theemitter optics directly. In other embodiments, the beam undergoesfurther conditioning prior to the emitter. In the illustratedembodiment, the coupler exit 709 is optically coupled to a beam shuffler602. An embodiment of the beam shuffler 602 is illustrated in FIG. 8.

The beam shuffler 602 comprises a fiber bundle having an inputarrangement 801 and an output arrangement 802. The fiber bundlecomprises a plurality of optical fibers 803 having input surfacesoptically coupled to the output surface 709 of the beam coupler 601. Theoptical fibers 803 may be made of the same material as the coupler 601,or other material having a similar index of refraction, n₃. In someembodiments, the optical fibers 803 lack claddings or have reducedcladdings to reduce the space between fibers 803 and reduce light lossat the interface between output surface 709 and the input 801.

The output fiber bundle arrangement 802 differs from the input fiberbundle arrangement 801 in a manner adapted to provide an outputintensity distribution 805. As discussed above, in some embodiments,each module FOV has an inner radius and an outer radius. In some cases,the inner radius and outer radius can differ by several kilometers.Accordingly, if the beam had isotropic intensity, the irradiance of thedetection zone near the outer radius could be significantly less thanthe irradiance near the inner radius. Indeed, any symmetric distribution708 provides an unequal irradiance throughout the detection zone. Toreduce these effects, the output fiber bundle arrangement 802 isconfigured to provide an asymmetrical spatial intensity profile 805. Theasymmetrical intensity profile is formed because fibers 808, 809 with aninput near the peak input intensities 806, 807 have outputs at locationscorresponding to farther detection distances. Any desired outputintensity function 805 may be obtained by such reshuffling. For example,the output intensity function 805 may be a monotonically decreasingintensity function. Additionally, in some embodiments, the centers ofthe fibers 803 are not symmetrically distributed about the center of theinput 708. Accordingly, the input intensity function 708 is sampled bythe fiber bundle 801 asymmetrically. This allows the output intensityfunction 805 to more accurately approximate a desired profile. Forexample, in the illustrated embodiment, fiber 808 is closer to the peakintensity value than fiber 809. Accordingly, fiber 808 samples a higherintensity value 806 than intensity value 807 sampled by fiber 809. Inother embodiments, shuffler 602 may include fiber optic couplers joiningtwo input fibers 803 to form a single output fiber 810. In suchembodiments, the exit intensity from the output fiber 810 may be the sumof the input intensities of the two input fibers 803.

After transmission through the emitter optics, the spatial intensityfunction 805 is transformed into a radiant intensity function. Inparticular embodiments, the radiant intensity function is or is anapproximation of the radiant intensity function (measured in Watts persteradian, or W/sr):

$\begin{matrix}{{{{J(\theta)} \propto R^{2}};{R = \frac{h}{\cos\;\theta}}},} & \left( {8{ab}} \right)\end{matrix}$where h is the approximate height of the system and θ is the verticalbeam angle with respect to the mast. FIG. 9 illustrates this geometry inthe context of an example platform on a mast 902 with inner detectionradius R₁ of 5 km and an outer detection radius, R₂ of 15 km. Here, h isthe height in the z direction. The x coordinate illustrates distancefrom the transmitter T_(x), where y would refer to the lateralcoordinate. θ is the vertical angle measured from the mast. At R₁ theangle is θ₁, at R₂ the angle is θ₂ and the difference between the anglesis Δθ. Additionally, β is the complement of θ and measures the anglefrom sea level to T_(x). FIG. 9 further illustrates, an example targetA_(T) just within range of Tx.

In this geometry, the emittance as a function of R is (ignoringatmospheric effects):

$\begin{matrix}{{E(R)} = {\frac{{J(\theta)}\cos\;\beta}{R^{2}}.}} & (9)\end{matrix}$Accordingly, the radiant intensity given in Eq. (8ab) compensates forthe dependence of E(R) on R⁻². For marine platforms: β<<1, so that J(θ)is as follows:

$\begin{matrix}{{J(\theta)} = {\frac{P_{o}}{\Delta\phi}\frac{F\left( {\theta_{1},\theta_{2}} \right)}{\cos^{2}\theta}}} & (10)\end{matrix}$where P_(O) is total beam power, Δϕ is beam azimuthal range of a singlefacet, and F-factor, is

$\begin{matrix}{{F\left( {\theta_{1},\theta_{2}} \right)} = \frac{h}{R_{2} - R_{1}}} & (11)\end{matrix}$including R-formula, as in Eq. (8b). Eq. (10) includes both R²-profileas in Eq. (8a) and power normalization, while

$\begin{matrix}{{\Delta\varphi} = \frac{w}{R}} & (12)\end{matrix}$where w is azimuthal range value. The azimuthal range may vary dependingon embodiment, but remains less than a threshold, w_(T), defined by theimplementation. This can be done, at least, in two ways, either keepingΔφ constant, or w constant, where the first case can be preferable inorder to keep well-controlled total FOV combined of a number of modules.In such a case, w-value will be variable, equal to w_(T)-value, forR=R₂:

In other implementations, the system may be mounted at other locations.For example, the system may be mounted on an aircraft or helicopter. Insuch an example, β may be not be <<1. In these implementations, J(θ)will vary, but may be determined in a straightforward extension of theabove analysis.

Additionally, although discussed in terms of a multimode fiber deliverypath 502. A coupler 601 and shuffler 602 may likewise be applied in thecase of a free space path 502. Additionally, in embodiments withoutlarge power requirements, the path 502 may comprise a single mode fiber.In these embodiments, the coupler 601 and shuffler 602 may or may not beapplied, depending on implementation.

Returning to FIGS. 5 and 6, the output 811 of the beam shuffler isdirected into emitter optics 504. In some embodiments, the emitteroptics comprises a collimating lens system. FIG. 10 illustrates anexample collimating lens system. In this figure, the fiber 1010 withcore diameter, d_(F), is illustrated. For example, the fiber 1010 may bethe output fiber bundle of the shuffler 602, or if a shuffler 602 is notemployed, the output of the beam expander 601. In still furtherembodiments, neither a beam expander 601 nor a shuffler 602 areemployed, and the fiber 1010 is the output of the beam path 502. In oneembodiment, d_(F)=(d_(F))_(min)=290 μm=0.29 mm, with (N_(A))=0.4; thus,f#=1.14, and, D/2f=0.44:

$\begin{matrix}{{f = {\frac{d_{F}}{\Delta\phi} = {\frac{0.29\mspace{14mu}{mm}}{0.0066} = {44\mspace{14mu}{mm}}}}};{D = {\frac{f}{f^{\#}} = {\frac{44\mspace{14mu}{mm}}{1.14} = {38.6\mspace{14mu}{mm}}}}}} & (13)\end{matrix}$The following general relation for multi-mode fiber optics applies:

$\begin{matrix}{{{4\; f\#^{2}} + 1} = \frac{1}{\left( N_{A} \right)^{2}}} & (14)\end{matrix}$From this relation: (N_(A))=0.447 for f#=1, and f#=1.14 for (N_(A))=0.4,while, the Ettendue theorem has the form:2d _(F)(N _(A))=(Δϕ)·D  (15)This is the optical version of the 2^(nd) principle of Thermodynamics,which is a consequence of the Liouville Theorem.

Bottom intensity value 1030, is transformed to the same upper (or,double-rescaled) exit angular intensity value 1030, as it is shown forthe three upper exit values 1030; same with intensity values 1031. Thisoccurs because the spatial intensity values 1032, for z-coordinated atthe exit of fiber core 1010, are transformed to angular intensity values1033 at the lens exit, and this relation is inverse (i.e., upside-down).

In some embodiments, an actuator 1034 may be coupled to the fiber 1010.For example, the actuator 1034 may comprise a piezoelectric actuator.This may be used to change the position of the beam axis 1039, forexample, in the z direction. As a result, the scanning range (R₁, R₂)may be modified. For example, the range might be modified from (5 km, 15km) to (8 km, 18 km).

Returning to FIG. 9, an example of calculating radiant intensity at thefar range of an embodiment is provided. Eq. (10) becomes:

$\begin{matrix}{{J(\theta)} = {\frac{P_{o}}{\Delta\phi}\frac{1}{\frac{1}{\cos\;\theta_{2}} - \frac{1}{\cos\;\theta_{1}}}\left( \frac{1}{\cos^{2}\theta} \right)}} & (16)\end{matrix}$To calculate the radiant intensity, J(θ), for R=15 km, assuming R₁=5 km,R₂=15 km, w=100 m, and P_(O)=6.667·10⁶ W, and:

$\begin{matrix}{{\Delta\phi} = {\frac{W}{R_{2}} = {\frac{100\mspace{14mu} m}{15\mspace{14mu}{km}} = {0.00666 = {0.382{^\circ}}}}}} & (17)\end{matrix}$And, equivalent pulse energy, E_(O), is (for τ_(L)=6 nsec)E _(O)=τ_(L) ·P _(O)=(6.667·10⁶ W)(6·10⁻⁹ sec)=40 mJ  (18)Also, assuming nominal repetition frequency value of n_(O)=100 Hz,according to Eq. (3), the equivalent continuous-work (CW) power, P, isP=P _(O) n _(O)τ_(L) =E _(o) ·n _(O)=(40·10⁻³J)(100 Hz)=4 W  (19)For R=R₂=15 km, Eq. (16) becomes

$\begin{matrix}{{J(\theta)} = {\frac{P_{o}}{\Delta\phi}\left( \frac{1}{{\cos\;\theta_{1}} - {\cos\;\theta_{2}}} \right)\left( \frac{\cos\;\theta_{2}}{\cos\;\theta_{1}} \right)}} & (20)\end{matrix}$where θ₁=89.43° (5 km) and θ₂=89.8° (15 km). Using Eq. (17), the valueof radiant intensity at the front of the target 901 is:

$\begin{matrix}{{J(\theta)} = {{{\left( \frac{{6.67 \cdot 10^{6}}\mspace{14mu} W}{0.00666} \right)\left( \frac{1}{{\cos\; 89.43{^\circ}} - {\cos\; 89.8{^\circ}}} \right)\left( \frac{\cos\; 89.43{^\circ}}{\cos\; 89.8{^\circ}} \right)}=={\left( {10^{9}\mspace{14mu} W} \right)(155)(2.84)}} = {{4.41 \cdot 10^{11}}\mspace{14mu}{W/{sr}}}}} & (21)\end{matrix}$In some cases, the target 901 is a non-Lambertian reflecting opticalsystem (such as a periscope). Such targets 901 may be calledoptical-augmented devices (OADs) herein.

FIGS. 11A-D illustrate various detection subsystems implemented inaccordance with various embodiments. Each system's detection subsystemdetects and processes laser pulses reflected from the module's FOV. Insome implementations, a single detection subsystem is sufficient, whilein other implementations multiple subsystems or subsystem branches maybe employed.

The illumination and optical power at the detector relates to theillumination and optical power at the reflector as follows.

$\begin{matrix}{{\eta_{DR} = {\frac{P_{5}}{P_{3}} = \frac{A_{L}}{\pi\; R^{2}\sin^{2}\alpha}}};{A_{L} = \frac{\pi\; D^{2}}{4}}} & \left( {22{ab}} \right)\end{matrix}$where D is the lens diameter, R the distance from reflector to detector,and α is the reflection divergence half-angle. P₅ is the power at thedetector while P₃ is the power at the reflector surface. For(Lambertian) clutter reflectors (using prime to distinguish clutterobjects):α′=90°  (23)while, for the target (non-Lambertian), α<<1, such as:α=0.25°=0.0044=4.4·10⁻³  (24)

From well-known radiometric definitions:P ₅ =E ₅ A ₅ ;P ₃ =E ₃ A ₃  (25ab)where E is illumination or irradiance. Therefore, substituting Eq. (25b)into Eq. (22a), we obtain

$\begin{matrix}{P_{5} = \frac{E_{3} \cdot A_{3} \cdot A_{L}}{\pi\; R^{2}\sin^{2}\alpha}} & (26)\end{matrix}$introducing focal length of the detection optics and systemmagnification results in:

$\begin{matrix}{P_{5} = \frac{E_{3} \cdot A_{5} \cdot A_{L}}{\pi\; f^{2}\sin^{2}\alpha}} & (27)\end{matrix}$or,

$\begin{matrix}{\frac{P_{5}}{A_{5}} = {E_{5} = \frac{E_{3} \cdot A_{L}}{\pi\; f^{2}\sin^{2}\alpha}}} & (28)\end{matrix}$Introducing brightness (or radiance), B₃, at the reflector then, thewell-known basic radiometric formula results:

$\begin{matrix}{E_{5} = \frac{B_{3} \cdot A_{L}}{f^{2}}} & (29)\end{matrix}$This formula shows that the retro-reflectors, such as periscopes, whichhave high brightness, image very well. However, they image into a verysmall spot, which is typically much smaller than pixel size (linear), a.

An example is a periscope cross-section as a reflector object, withdiameter, d=7 cm. Assuming typical: R=10 km, and f=30 cm, then the imagesizes is:

$\begin{matrix}{{s = {\frac{d}{m} = {\frac{7\mspace{14mu}{cm}}{3.33 \cdot 10^{4}} = {{{2.1 \cdot 10^{- 4}}\mspace{14mu}{cm}} = {2.1\mspace{14mu}{µm}}}}}},} & (30)\end{matrix}$where m is demagnification (m=R/f). If a 50 μm sensor (pixel) size isused (i.e., a=50 μm), then:

$\begin{matrix}{\frac{a}{s} = {\frac{50}{2.1} = 23.8}} & (31)\end{matrix}$i.e., periscope cross-section cannot be imaged (in other words, thesystem is a pseudo-imaging system, where the target images do notsatisfy the resolving criteria of having images extending across atleast two sensors).

The ratio of clutter/target powers, may be written as

$\begin{matrix}{\frac{P_{5}}{P_{5}^{\prime}} = \frac{\frac{E_{3}A_{5}A_{L}}{\pi\; f^{2}\sin^{2}\alpha}}{\frac{E_{3}^{\prime}A_{5}^{\prime}A_{L}}{\pi\;{f^{2}(1)}}}} & (32)\end{matrix}$Additionally:E ₃ =r E ₂ ;E ₃ ′=r′E ₂′  (33ab)where subscript “3” denotes the exit plane of the reflector plane, whilesubscript “2” denotes the entrance plane of the reflector, and r and r′are Fresnel (energy) effective reflection coefficients for target andclutter, respectively. Thus:

$\begin{matrix}{\frac{P_{5}}{P_{5}^{\prime}} = {\frac{\frac{{rE}_{2}A_{5}A_{L}}{\pi\; f^{2}\sin^{2}\alpha}}{\frac{r^{\prime}E_{2}^{\prime}A_{5}^{\prime}A_{L}}{\pi\;{f^{2}(1)}}} = {\left( \frac{A_{5}}{A_{5}^{\prime}} \right)\left( \frac{1}{\sin\;\alpha} \right)\left( \frac{r}{r^{\prime}} \right)}}} & (34)\end{matrix}$where, E₂=E₂′ (e.g, the same laser illumination is incident on targetand clutter), and clutter reflection beam is imaged, uniformly; i.e.,filling up whole pixel area; thus,A ₅ ′=a ².  (35)Accordingly:

$\begin{matrix}{\frac{P_{5}}{P_{5}^{\prime}} = {\left( \frac{A_{3}}{m^{2}} \right)\left( \frac{1}{a^{2}} \right)\left( \frac{1}{\sin^{2}\alpha} \right)\left( \frac{r}{r^{\prime}} \right)}} & (36)\end{matrix}$Introducing the resolving element, as described herein:

$\begin{matrix}{{\frac{P_{5}}{P_{5}^{\prime}} = {\frac{A_{3}}{\left( {\delta\; l} \right)^{2}}\left( \frac{1}{\sin^{2}\alpha} \right)\left( \frac{r}{r^{\prime}} \right)}},} & (37)\end{matrix}$where δl is the pixel resolving element (in other words δl is the sizeof an object that is imaged to the size of the pixel) (δl=m*A), and, forcircular periscopic cross-section with diameter, d:

$\begin{matrix}{A_{3} = \frac{\pi\; d^{2}}{4}} & (38)\end{matrix}$and, Eq. (37) becomes,

$\begin{matrix}{\frac{P_{5}}{P_{5}^{\prime}} = {{\left( \frac{\pi\; d^{2}}{4} \right)\left\lbrack \frac{1}{\left( {\delta\; l} \right)^{2}\sin^{2}\alpha} \right\rbrack}{\left( \frac{r}{r^{\prime}} \right).}}} & (39)\end{matrix}$

As an example, the resolving element for δl, for a=50 μm, f=20 cm, andR=10 cm is:(δl)=ma=(50 μm)(5·10⁴)=25·10⁵ μm=25·10² mm=2.5 m  (40)

To continue this example, the power ratio for (δl)=2.5 m, d=7 cm, andα=1°, assuming: r=r is:

$\begin{matrix}{\frac{P_{5}}{P_{5}^{\prime}} = {{\frac{\left( {38.46\mspace{14mu}{cm}^{2}} \right)}{\left( {2.5\mspace{14mu} m} \right)^{2}}\left( {3\text{,}283} \right)} = {{\frac{(38.46)\left( 10^{- 4} \right)}{(2.5)^{2}}\left( {3.28 \cdot 10^{3}} \right)} = {{(20.2)\left( 10^{- 1} \right)} = {2.2.}}}}} & (41)\end{matrix}$Accordingly, voxel inference (i.e., distinguishing a true target from apotential false target using the presence of a reference clutter signal)may be applied in this example because both powers have comparablevalues. In general, so long as the power ratio for the clutter signalsand potential target signals are within the dynamic range of thedetector, both signals may be read by a single detector.

As a contrary example, assume: f=30 cm, a=20 μm, α−0.25°, R=10 km, d=7cm, and r=r′. Here the power ratio of retroreflected target signal toLambertian clutter signal is

$\begin{matrix}{\frac{P_{5}}{P_{5}^{\prime}} = {{\frac{38.46\mspace{14mu}{cm}^{2}}{\left( {66\mspace{14mu}{cm}} \right)^{2}}\left( {52\text{,}500} \right)} = {463.5 ⪢ 1}}} & (42)\end{matrix}$This power ratio exceeds typical dynamic ranges of availablephotodetectors, and hence voxel inference cannot be applied using asingle detection branch.

Accordingly, for small a-angles and small-δl, the target power is muchhigher than that for reference clutter; thus, the voxel inference cannotbe applied within the single system; otherwise the voxel inference(within the same system) can be applied.

This reflects the general fact that minimizing both false negatives andfalse positives within a single detection system may be contradictory.In general, to minimize false negatives, the target signal is maximizedby reducing sensor size, a. This also reduces the NEP (noise equivalentpower) of the system.

In contrast, to minimize false positives, ability to perform voxelinference is maximized; e.g., both signal and clutter powers are broughtwithin the system detector range.

An R* parameter may be defined as the distance, that:P=P′;r=r′  (43ab)The use of equality for R* is for simplicity of explanation. In general,the relevant distance is where both powers are within the systemdetection range.

As an example, typical conditions might be d=7 cm, α=1°, f=20 cm, anda=50 μm. The R* value is obtained from

$\left( {\delta\; l} \right)^{2} = {\frac{\left( \frac{\pi\; d^{2}}{4} \right)}{\sin^{2}\alpha} = {{\left( {38.48\mspace{14mu}{cm}^{2}} \right)\left( {3\text{,}283} \right)} = {{126\text{,}330\mspace{14mu}{cm}^{2}} = {{126\text{,}{330 \cdot 10^{- 4}}\mspace{14mu} m^{2}} = {12.63\mspace{14mu} m^{2}}}}}}$Thus,(δl)=3.55 m  (44)and,

$m = {\left( \frac{\delta\; l}{a} \right) = {\frac{3.55\mspace{14mu} m}{50\mspace{14mu}{µm}} = {\frac{{3.55 \cdot 10^{6}}\mspace{14mu}{µm}}{50\mspace{14mu}{µm}} = {7.1 \cdot 10^{4}}}}}$thus, the R*-value, isR*=f·m=(20 cm)(7.1·10⁴)=142·10⁴ cm=142·10² m=14.2 km  (45)Less than this distance, P>P′, while greater than this distance, P′>P.From Eq. 39:

$\begin{matrix}{{R^{*} = {{\frac{\sqrt{A_{3}}}{\sin\;\alpha}\left( \frac{f}{a} \right)} = {\sqrt{\frac{\pi\; d^{2}}{4}}\left( \frac{1}{\sin\;\alpha} \right)\left( \frac{f}{a} \right)}}}{{and}\text{:}}} & (46) \\{R^{*} = {{\frac{\sqrt{\pi}}{2}\left( \frac{d}{\sin\;\alpha} \right)\left( \frac{f}{a} \right)} = {(0.89)\left( \frac{d}{\sin\;\alpha} \right)\left( \frac{f}{a} \right)}}} & (47)\end{matrix}$To increase the ability to perform voxel inference, the referenceclutter signal must be reduced in respect to target signal by reducingthe R* value. Therefore, according to Eq. (47), adjustment of followingparameters in the following manner minimizes R* value:d

;α

;f

;a

  (48abcd)Conditions (48ab) are fixed for specific target (e.g., periscope) types,so system parameters determining Eq. (48cd) may be modified. Reducingf-value, is equivalent to reducing system sensitivity because reducing fvalue is equivalent to reducing D value in the f# (i.e., weakening lightcollection). Accordingly, preferably, the sensor (i.e., pixel) size a isincreased to reduce R*. Additionally, a second system having a differenta value will have a different R* value. Accordingly, in someimplementations, two parallel detection systems are used for distancesshorter than R<R*.

Minimizing both false negatives and false positives at the same time isa central challenge with the IOS. This is done by maximizing thestrength of the laser beam reflected from the periscopic target, and, atthe same time, providing voxel inference (i.e., to process informationfrom clutter correlated to the target, which includes, for example, thebody of periscope, wave disturbance by the submarine, etc.) The firsttask leading to minimization of false negatives [target misses] isdetecting the signal from the target. This is performed, in oneembodiment, for example, by elements 1103 and 1104 in the upper branchof the detection system of FIG. 11D. It can also be performed by thecorresponding elements in the upper branch of FIGS. 11B and 11C.

The second task [signal from correlated clutter] leading to minimizationof false positives [false alarms] relates to detecting a signal fromcorrelative clutter. This task is performed, for example, by elements1109, 1103′ and 1104′ in the lower branch of detection system in FIG.11D (or in the corresponding elements of FIGS. 11B and 110). In idealcase, the powers attained in both branches are the same or close to eachother, which means that P=P′ as in equation 43a. The equality isrealized at a distance, R=R*, as in equation 47. For R>R*, we obtain Psmaller than P′, while for R<R* we obtain P>P′. Therefore and because Pis typically larger than P′, a goal of the system is to minimize the R*value to increase the range of operation of voxel inference. However, incircumstances where P′ is larger than P, the system can be configured toprovide the inverse operation.

According to equation 47, the only parameters that can be controlled orvaried by modifying the system are f and a, where f is focal length, anda is the linear pixel size. In order to increase the value of P′ in thelower branch of FIG. 11D, we need to increase the a value or reduce thef value, or both. This leads to increasing the pixel resolving elementdefined by equation 40. For too small a, which is pixel linear size, alarger pixel size is used in detector array PDA 1103′ in the lowerbranch. In some embodiments, the pixel size used in PDA 1103′ is chosenas greater than the pixel size in PDA 1103. Accordingly, variousembodiments use two pixel sizes—a smaller pixel size in the upperbranch, and a larger in the lower branch

Depending on system configuration and constraints, componentavailabilities and other design considerations, it may not always bepossible or practical to implement detectors 1103, 1103′ with actualpixel sizes meeting this constraint. Accordingly, in some embodiments, apixel cluster concept can be applied in the lower branch in whichmultiple adjacent pixels are clustered together to yield a largereffective pixel size. For example, four (2×2), nine (3×3), (they neednot be in a ‘square’ array) or more pixels can be configured to work incoordination as one single pixel. This electronically increases pixelsize in the lower branch.

The pupil 1109 in the lower branch of FIG. 11D may be included toprovide an equivalent decrease of diameter, D, of the collection lens.Then, keeping as typically fixed f#=f/D can allow a decrease in the fvalue of the same amount, or approximately the same. For example, if Dis decreased 1.5 times, then the f value can also be decreased 1.5times. Thus, we obtain cumulating effect of decreasing R* value, thusminimizing both false negatives and false positives. This is becausethere could be a lot of strong reflective signals, but by using thesecond parallel branch with a regulated pupil 1109, false signals thatdo not have properly correlative clutter can be reduced or eliminated.This means reducing or even eliminating false alarms.

The detection subsystem may comprise a filter 1101. The filter 1101passes the laser wavelength while blocking other light. This reduces,minimizes, or eliminates optical noise. For example, such optical noisemight arise from unwanted solar reflections, or other light sources.Because the laser beam is practically monochromatic, the filter 1101 maybe a narrow wavelength filter. For example, the filter 1101 may comprisean interference passband filter, such as a Bragg filter. These filtersdemonstrate a “blue-shift” effect for slanted beams, the form:λ=λ_(O)√{square root over (1−sin² α/n²)}, where a is the slant angleλ_(O) is interference wavelength under normal incidence (α=0). Thisblue-shift effect can be quite significant for narrow passband filtersand moderate incidence angles. However, as discussed above, in someembodiments, each flash FOV may be less than 1°, for example 0.36°. Theblue shift effect in these cases is small enough that the interferencefilter performance is not compromised. For example, for α=0.36°,Δλ=0.012 nm.

In further embodiments, the filter 1101 may comprise a polarizingfilter. As discussed above, in some embodiments, the emitted light beammay have a polarization signature. The filter 1101 may be configured toallow only light having that polarization signature to pass. Forexample, if the emitted beam is TH-polarized, the filter 1101 maycomprise a TH-polarization filter. Man-made targets may be more likelyto reflect light without change in polarization when compared to naturalclutter, such as waves and plant matter. Accordingly, filter 1101 mayincrease the likelihood of target detection by reducing cluttersignatures.

In still further embodiments, the filter 1101 may comprise a non-uniformneutral density filter. A non-uniform neutral density filter 1101 may beused instead of or to augment the normalizing system of the emitter. Forexample, the non-uniform neutral density filter 1101 may reduce theoptical signal from close objects to normalize the received signal.

In the illustrated embodiment, the detection optics 1102 is opticallycoupled to the filter 1101. In some embodiments, the detection optics1102 is disposed behind the filter 1101 in the optical path. In otherembodiments, the detection optics 1102 may be in front of the filter1101. The detection optics 1102 is configured to transfer received lightto the detector 1103 in a pseudo-imaging manner. In still furtherembodiments, a filter 1101 is not employed.

In some embodiments, the detection system comprises a pupil 1109 coupledto, or integrated with, the optics 1102. In the optical path, the pupil1109 may be behind or in front of optics 1102. The pupil 1109 may beused in the system to control the effective aperture, and thus, f#, ofthe optics system 1102. In embodiments having a pupil 1109, the pupil1109 may be used to control the instantaneous dynamic range of thedetection system. In some instances, reflected signals may exceed thesystem dynamic range—for example, if an object with a strong reflected(e.g., a non-Lambertian reflector) signal is near clutter with weakerreflected signal (e.g. a painted marine vessel). In such a case, thepupil may be used to reduce the light gathering ability of the opticssystem 1102, to bring the reflected signals within the dynamic range ofthe detector 1103.

In some embodiments, the pupil 1109 is adjustable, and to control the f#of the system, the detection optics 1102 has an adjustable focal length,f. For example, in some embodiments, the f# may be between 1 and 5. Insystems without a pupil 1109 or with a fixed pupil 1109, the focallength f of the detection optics 1102 may also be fixed to set thedesired f#.

As discussed below, the detector 1103 may comprise a one or twodimensional array of individual sensors 1106 separated by gaps (FIG.12A). Alternatively, the detector 1103 may comprise an array of rows ofgapless one dimensional sensor 1106 arrays (FIG. 12B). The detectionoptics 1102 is configured to transmit light to the detector 1106 in amanner that avoids a possible detection signal falling into the gapsbetween sensors 1106.

In the case of long distance detection, such as optical periscopedetection (OPD), the photodetector array 1103 creates potential problemwith missing periscope target during pseudo-imaging operation. This isbecause, the periscopic target is very small, with 10 cm-diameter, forexample. In such a case, its image, at very long distances (e.g., R=10km), is very small, down to even 0.1 μm size. Then, if photodetectorarray 1103 filling factor, F (i.e, the ratio between sensor area tototal array area), is not perfect (i.e., F=100%), this target image canbe missed in the space between sensors 1106. This is illustrated in FIG.12A, where a is the sensor 1106 size, and δa is the half-pitch betweensensors. Thus, the filling factor, is:

$\begin{matrix}{F = {\frac{a}{a + {\delta\; a}} = \frac{1}{1 + \frac{\delta\; a}{a}}}} & (49)\end{matrix}$In FIG. 12A, a photodetector 2D geometry is shown with a less than 100%filling factor (F<1). In such, if imaging optics with high resolutionwere used, the periscopic target image 1107 can be missed in the gapbetween sensors 1106. Assuming, for example, a=20 μm, and δa=0.1 μm, erelative pixel space is: (δa/a)=0.01/20=0.005, and F=0.995=99.5%; i.e.,even for such high filling factor, a small target can be missed.

In one embodiment, this problem is solved by increasing the size of thetarget signal at the detector 1103. FIGS. 13A-D illustrate an embodimentof detector optics 1103 that increases the size of the target signal.The optics system 1103 comprises a lens, lens system, catoptric system,or catadioptric system the aberrates the image by de-focusing of imageplane; i.e., providing that the image, equation is not well satisfied.Then, by artificially increasing target signal sizes to 1 μm, forexample, F=0.95=95%, and the previous filling factor (F=99.5%) may besatisfactory. Imaging optics in this highly-aberrated mode satisfy boththe etendue theorem (or, Liouville theorem) for concentrator optics,and, at the same time, optimize detector optics for maximum powercollection (and maximum electrical SNR). For example, in the illustratedembodiment, the detector 1102 may be positioned closer to or fartherfrom the optics system 1103 than the focal length of the optics system1103. In other embodiments, the optics system 1103 may have apredetermined type and magnitude of aberration to produce the desiredtarget signal sizes. In one embodiment, the detection optics 1102produces an image with a circle of confusion having a diameter as largeor larger than a distance between adjacent photodetectors 1106 of thephotodetector array 1103 (i.e., a radius greater than or equal to δa).For example, the radius of the circle of confusion may be one, two, orthree times larger than δa. In other embodiments, the circle ofconfusion is determined according to the photodetector 1106 size a. Forexample, the diameter of the circle of confusion may be equal to a. Inone embodiment, each sensor 1106 comprises an avalanche photo diode(APD), with a being about 25 μm. In a further embodiment, the pointspread function (PSF) exceeds the Airy ring by a factor of 5-10 (turninga 2 μm target image into a 10 20 μm-spot). In addition to reducing therisk that a target signal will fall on dead space between pixels, theaberrated imaging system may disperse the signal across multiple pixels,reducing overload when a strong target signal is present.

According to the Nyquist resolution criteria, the smallest resolvingobject should produce an image across at least two pixels 1106 of thearray 1103. If, for example, this object is a periscope cross-section,with 10 cm diameter, then for detection optics 1102, with focal lengthf=30 cm and distance, R=10 km, the system demagnification, m=R/f=10km/30 cm=3.33*10⁴. Then, the Nyquist-satisfying pixel size is equal to 5cm/3.33*10⁴=1.5 microns, i.e, smaller than the Raleigh resolution(1.22*λ*f#=1.59 microns, for f#=1 and λ=1.3 microns), and which iscomparable with speckle size for this system. Thus, in typicalconditions, such small objects cannot be imaged without significantspeckle-sized distortion. Therefore, the integrative optics system is“pseudo-imaging” rather than an imaging system. In other words, theoptics 1102 produces images of targets that do not satisfy the Nyquistcriteria for imaging a target.

In various embodiments, the f# of the optics system is as small aspossible. For example, the f# may be between 1 and 0.5. However, inother embodiments, f#s between 1 and 5, or even higher may be employed.

The size of the detector 1103 may depend on considerations such as thesensor 1106 size, the effective diameter of the optics system and thedistance from the detector 1103 to the optics (which may differ from thefocal length for de-focusing embodiments). For a lens system with aneffective diameter of D=30 cm, for example, f=30 cm, whileΔϕ=0.38°=0.0066; thus, Δϕ/2=0.0033, andd=Δϕ×f=(0.0066)(30 cm)=1.98 mm  (50)and, for vertical FOV (Δθ=0.37°), d=1.94 mm for 50 μm APD sensors (e.g.,1106, FIGS. 12A&B). Then, 1.98 mm=1980 μm; thus, the number ofhorizontal APD sensors is

$\begin{matrix}{{2N_{x}} = {\frac{1980}{50} = 40}} & (51)\end{matrix}$and, the number of vertical APD sensors is (e.g, in a APD detector array1103 (FIG. 12A)

$\begin{matrix}{{2N_{y}} = {\frac{1940}{50} = 39.}} & (52)\end{matrix}$

In some embodiments, the ratio of the sensed energy from a potentialtarget to the sensed energy from the surrounding clutter is used aparameter for target detection. The sensed area per image sensor 1106(i.e., the area illuminated by a flash whose reflection impinges on asensor 1106) is correlated to the sensed energy from the surroundingclutter. This parameter is dependent on factors such asde-magnification, FOV, sensor size, and distance from the sensed area tothe system.

In FIG. 13B, the detection optics system 1103 comprise a compoundparabolic concentrator 1301. In the illustrated embodiment, the detector1102 is coupled to the absorber plane 1302 of the concentrator 1301. Inother embodiments, the detection optics system 1103 may further compriseone or more lenses 1303 disposed between the concentrator 1301 and thedetector 1102 (FIG. 3C). In still further embodiments, the detectionoptics system 1103 may comprise an array of concentrators 1301 disposedbehind a lens or other optics system 1303. Individual sensors 1106 ofthe detector 1102 may be disposed at corresponding absorber planes 1302of the array of concentrators 1301 (FIG. 13D).

As illustrated in FIGS. 14A and 14B, in a further embodiment, thedetection optics system 1103 comprises one or more tapered opticalfibers 1401. For example, the optics system 1103 may comprise an arrayof tapered optical fibers 1401, each tapered fiber 1401 having an outputat a sensor 1106. This system directs more light onto the sensors 1106,avoiding signal falling in the dead space between sensors. In someembodiments, the tapered optical fibers 1401 may be utilized inconjunction with or in replacement to, the concentrators 1301 and thelens system 1103.

As discussed above, the detector 1103 may comprise a plurality ofindividual sensors 1106 arranged in various one or two dimensional pixelarrays. The sensors 1106 are selected to have a sufficient specificdetectivity. Typically, in semiconductor detectors 1106, the NEP (noiseequivalent power) is defined by so-called specific detectivity, D*, inW⁻¹ cm Hz^(1/2), by the following formula:

$\begin{matrix}{({NEP}) = \frac{\sqrt{A \cdot B}}{D^{*}}} & (53)\end{matrix}$where A is the photodetection area in cm² and B is the bandwidth in Hz.For semi-conductor detectors, D* is, approximately, proportional towavelength, up to cutoff wavelength, λ cutoff, defined by energy gap,Eg, as: λ cutoff=hc/Eg, where h is the Planck constant and c is thespeed of light. For Avalanche Photodiodes (APD), the speed is very high(even in picoseconds), but (NEP) is limited by Johnson (thermal) noise,where

$\begin{matrix}{{{r.m.s} = {\left\langle i_{n}^{2} \right\rangle = \frac{4\mspace{14mu}{kTB}}{R}}},} & (54)\end{matrix}$where < > is the statistical ensemble average, i_(n) is the noisecurrent, k is the Boltzmann constant, T is the temperature in Kelvins(K°) and R is the resistance (typically, R ˜20Ω). Then for typicalapplications, D* ˜1.9·10¹¹ Hz^(1/2) cm W⁻¹, and, for pulse laser withpulse length: δt=6 ns, the bandwidth B=1/δt=1.67·10⁸ Hz; and for APDpixel size: √{square root over (A)}=25 μm=25·10⁻⁴ cm and √{square rootover (B)}=1.3·10⁴ Hz^(1/2), from Eq. (35):

$\begin{matrix}{({NEP})_{o} = {\frac{\sqrt{A \cdot B}}{D^{*}} = {\frac{\left( {{25 \cdot 10^{- 4}}\mspace{14mu}{cm}} \right)\left( {{1.3 \cdot 10^{4}}\mspace{14mu}{Hz}^{1/2}} \right)}{{1.9 \cdot 10^{19}}\mspace{14mu}{Hz}^{1/2}{cm}\; W^{- 1}} = {{1.68 \cdot 10^{- 10}}\mspace{14mu} W}}}} & (55)\end{matrix}$In other embodiments, the sensors 1106 may comprise photomultipliers.With photomultipliers with very high gain ˜10⁷, the dark current noisedominates, and:

$\begin{matrix}{({NEP})_{{DARK}\mspace{14mu}{{CURRENT}{({D\; C})}}} = {\frac{4 \cdot 10^{- 17}}{\eta}\sqrt{B}W}} & (56)\end{matrix}$where η-quantum efficiency. Then, for η=0.8 and √{square root over(B)}=1.3·10⁴ Hz^(1/2):

$\begin{matrix}{{({NEP})_{D\; C} \cong \frac{{4 \cdot 10^{- 17} \cdot 1.3 \cdot 10^{4}}\mspace{14mu} W}{0.8}} = {{{6.5 \cdot 10^{- 13}}\mspace{14mu} W} = {0.65\mspace{14mu}{pW}}}} & (57)\end{matrix}$Accordingly, for typical embodiments, the NEP is assumed to beapproximately:(NEP)_(O)=0.5pW=0.5·10⁻¹² W=0.5·10⁻¹⁸MW=−183.01 dBM  (58)

In further embodiments, the detector 1103 may comprise a CCD array. CODshave slower responses than APDs but NEP is lower and CCD pixel sizes aresmaller. For example, for KODAK KAF-50100 Image Sensor, pixel sizes are6 μm×6 μm, and Maximum Data Rate, B=18 MHz; i.e., (100)/(18)=5.5 slowerthan required for some implementations. In particular, implementationsusing laser pulses with approximately 10 nsec length are equivalent toB=100 MHz. By comparison, CCD speed limitation allows to measure onlylaser pulses 5.5-times longer; i.e., 16.5 m vs. 3 m for APD devices(since, cδt=(3*10⁸ m/s)(10⁻⁸ m)=3 m). On the other hand, the SNR-valueis much better. This is, because, the CCDs are limited by dark currentnoise rather than by Johnson noise as the APDs are. As a result, theirD*-values are much higher: about 10¹² W⁻¹ cm Hz^(1/2) vs. 10⁹ W⁻¹ cmHz^(1/2) for APDs.

In still further embodiments, the detector 1103 may comprise a solidstate photomultiplier array.

The detection system further comprises detector electronics 1104 coupledto the detector 1103. In some embodiments, the detector electronics 1104may comprise normalizing electronics. For example, the normalizingelectronics may be used to normalize the gain settings across thedetector to supplement or replace the normalizing system of the emitter.For example, a non-linear detector response, following a generalsquare-root function or sigmoid function curve may be applied so thatdetector elements receiving light from closer objects have lower gainthan detector elements receiving light from farther objects.

In some embodiments, the detector electronics further comprise RISCprocessor arrays 1104. Each RISC processor 1108 of array 1104 is coupledto a plurality of sensors 1106 of detector 1103. In some embodiments,each RISC processor 1108 of array 1104 is coupled to a 3×2 grid of sixsensors 1106. In embodiments employing a 39×40 array of 50 μm APDsensors, an array of 256 RISC processors allows 255 RISC processors tobe coupled to 6 APDs each, and one RISC processor 1108 to be coupled to7 APDs. Each RISC processor 1108 receives a set of readouts from itsconnected APDs and performs a set number of operations on the set ofreadouts. In other embodiments, the detector electronics 1104 maycomprise any other combination of analog or digital electronics systems.

In one embodiment, the RISC processors 1108 perform novelty filtering ontheir readouts. During the novelty filtering operation, each readoutx_(i) is translated by some predetermined amount Δx to form a set oftranslated readouts x_(iO)=x_(j)+Δx. In other words, the x_(iO) has thesame coordinates as x_(i), but its value is the value of x_(j) at Δxaway. In some embodiments, the translation is performed using shiftregisters or other memory devices coupled to the processors 1108. Whenthe translated readouts are formed, the RISC processors 1108 send thetranslated readout values to the appropriate RISC processors. Forexample, if Δx is one unit down, then the RISC processor connected tothe APD at (1,1) would send the readout from (1,1) to the RISC processorconnected to the APD at (1,2).

Next, during the novelty filtering operation, each RISC processorsubtracts x_(i)−x_(io). If each readout is a binary value (for example,if the APD readout is treated as 1 if the APD detects more than athreshold amount of light and 0 if the detected amount of light is lessthan the threshold), this value will be 1 at edges of objects and 0within and outside objects. In some embodiments, the RISC processorarray 1104 outputs the subtracted readouts as a set of detected edges.In further embodiments, the RISC processor array 1104 performs furthercalculations.

In one embodiment, the RISC processor array 1104 calculates the squaredEuclidean distance d_(E) ², in the form; shown in N-space:

$\begin{matrix}{d_{E}^{2} = {\sum\limits_{i = 1}^{N}{\left( {x_{i} - x_{i\; o}} \right)^{2}.}}} & (59)\end{matrix}$This value d_(E) ² may be output by the RISC processor array 1104. Invarious implementations, the squared Euclidean distance may becalculated for an entire sensor readout, for a row of sensors, for acolumn of sensors, or for a block of sensors connected by detectededges.

These examples are intra-frame calculations (i.e., calculationsperformed on a single readout of the detector 1103). In furtherembodiments, the RISC processor array 1104 may perform inter-framecalculations (i.e., calculations performed on multiple readouts of thedetector 1103). Examples of such inter-frame calculations are describedin further detail below.

The RISC processor array 1104 is coupled to a detection processor 1105.The detection processor 1105 receives data from the RISC processor array1104 and performs various detection algorithms to determine if a targetis detected. Examples of such detection algorithms are described infurther detail below.

In further embodiments, parallel detection systems may be used tomeasure return flashes. FIG. 11B illustrates such an embodiment. In thisembodiment, a first detection subsystem 1000 is configured to detectpossible target signals, while a second detection subsystem 1120 isconfigured to detect possible reference clutter signals. In someimplementations, the possible target signals are signals with high powerreflections from non-Lambertian reflectors. For example, possible targetsignals may arise from ocular retroreflectors, such as binoculars orperiscopes, or from other environmental features, such as causticscaused by waves. Reference clutter signals may comprise clutter signalsthat characteristically occur in proximity to true target signals. Forexample, for a periscope target, the reference clutter signals maycomprise characteristic reflections from the periscope body or thesubmarine body. The reference clutter signals may be used by the signalsto determine which of the possible target signals are true targetsignals. Such an implementation may be employed, for example, if thereflection signal strength from clutter objects, and in particular,reference clutter objects, is significantly different than thereflection signal strength from possible target objects. For example, ifthe reflection coefficient from a potential target object is muchgreater than the reflection coefficient from the surrounding referenceclutter, a single detector 1103 may not be able to detect both signals.

In this embodiment, if filters 1101 and 1111 are employed, they may havesimilar filter characteristics. Subsystem 1000 is configured to haveless greater light gathering ability, in order to detect the weaker ofthe potential target signals and clutter signals. Accordingly, thesystem 1000 lacks a pupil. Additionally, the detector 1103 may havelarger sensor sizes than detector 1113, such as 50 μm compared to 25 μm(linear size). The detection optics 1112 may vary from detection optics1102 to accommodate the pupil 1119. For example, the focal length ofdetection optics 1112 may be longer than the focal length of detectionoptics 1102 to accommodate the reduced diameter caused by pupil 1119.

The detector electronics 1104, 1114 may be any combination of digital oranalog circuitry, including RISC processors, sufficient to provide thevoxel readouts to the detection processor 1105. Additionally, in someembodiments, detectors 1103 and 1113 may share some detector electronics1104, 1114, components, for example, to combine the signals prior toproviding the signals to detection processor 1105.

FIG. 15 illustrates a method of operation of a system module, such asmodule 206, 207. In step 1501, the system emits a first pulse toilluminate a first facet of the module's field of view. As discussedabove, field of view of the module is divided into facets, with eachfacet illuminated by a single laser flash. For example, a systemproviding a 360° field of view may comprise 10 modules, each with a 36°field of view. Additionally, each module may use 100 facet flashes tocover the 36° field of view, so that each facet flash illuminates atleast 0.36°. In some embodiments, the laser has an energy of about 40 mJper pulse and an effective pulse length of τ_(L)=6 ns, providing a pulsepower of about 6.667*10⁶ W. In embodiments employing eye-safe lasers,the laser wavelength may be greater than 1 μm, and in particular,greater than 1.3 μm, or greater than 1.6 μm. In some embodiments, themodule emits multiple pulses per facet. In these cases, step 1501 may berepeated multiple times.

In step 1502, the system stabilizes the emitter and detector whiledetecting return pulses from objects within the facet field of view. Asdiscussed above (for example, see FIG. 9) the area of detection is oftenan annular section, for example, with an inner radius around 5 km and anouter radius around 15 km. Accordingly, in this example, return pulsesfrom objects within the detection zone may take between 10 km/c≈0.033 msand 30 km/c≈1 ms. The module is stabilized for the total time ofpossible return pulses so that sensors within the detector do notreceive signals from objects at multiple locations within the detectionzone.

The step 1502 of receiving return pulses further comprises time-gatingthe sensor readouts. Time gating the sensor readouts allows the systemto determine the distance from the module to the object or clutter thatreflected the laser pulse. Then, the minimum quantum of distance, δz,resolved by each laser pulse, is: δz=(0.5)cδt, where c=3·10⁸ m/sec isspeed of light in air (vacuum) and δt is the pulse width (for example,full width at half maximum). For example, for δt=10 nsec=10⁻⁸ sec:δz=1.5 m, while for δt=1 nsec, δz=15 cm. The step of gating 1502 maycomprise gating the detector at any rate up to the pulse repetition rateto obtain a desired distance resolution. The set of time gated sensorreadouts, indexed by time, will be termed a set of voxels. Each pixel(i.e., sensor) has its voxel derivatives; each voxel with sizes: a_(x),a_(y), δz, where a_(x), a_(y)—are pixel sizes, while δz is the temporal(i.e., distance) resolution. It should be noted that this is anapproximation based on a system mounted at height h that is smallcompared to the distance R between the system and the target. Systems,such as aircraft or helicopter mounted systems, where the height h islarge or on the order of R. δz may be replaced with δR, which providesnon-orthogonal voxels, with sizes a_(x), a_(y), δR. Alternatively, suchsystems may translate the δR values to δz values. In these systems β(FIG. 9) may be large, requiring an appropriate modification to theenergy detection normalization set-up.

The module waits for at least the maximum return time for pulses toreturn from the farthest range of the detection zone. Then, in step1503, the module translate the next facet and repeats the method. Forranges on the order of 15 km, the maximum return times will be around0.1 msec. Accordingly, the maximum repetition rate is about 10 kHz forone laser pulse per facet. However, lasers meeting the requisite powerparameters typically have maximum repetition rates of about 100-200 Hz.Additionally, in some embodiments, multiple pulses are emitted perfacet. A 100 Hz laser frequency allows emission of one pulse per facetand a scan rate of 100 facets per second. Allowing a module with a 38°field of view and 100 facets to have a scan rate of 1 scan/sec.

In this example, with one module FOV per second, (f=1 Hz) assuminghorizontal mechanical tracking with N=100 channels, there are n⁻¹=10msec between facets, which is achievable by current mechanical systems.Total return time, Δt, is much smaller than tracking-step-time (TST):(Δt)<<(TST)=n ⁻¹  (60)since Δt=10⁻⁴ sec, while (TST)=10⁻² sec. Therefore, the mechanicaltracking system can be relatively stable, since, there is a lot of timefor stabilization. In this example, 99% of the time, the laser is notoperating; so, this time can be used for stabilization purposes.

FIG. 16 illustrates a method of target detection implemented by a systemmodule. For example, this method may be performed by a detectionprocessor 1105, RISC array 1104, or detection processor 1105 incombination with RISC array 1104. In step 1601, a set of voxels areobtained for processing. In some implementations, the set of voxels area set of voxels from one facet of the module. In other implementations,the set of voxels may be obtained from some or all of the facets of themodule. In some embodiments, the set of voxels may have been previouslynovelty filtered or otherwise processed by RISC array 1104.

In some cases, the set of voxels obtained in step 1601 depends on theenvironmental visibility. The atmospheric attenuation, T_(A), may impactthe detection range or the total detection space. T_(A) is theatmospheric attenuation in the form:T _(A) =e ^(−σR)  (61)where R-distance from laser delivery sub-system to the target, and σ isatmospheric attenuation coefficient, based on the following well-knownphenomenological formula (defined as distance, V, where image contrastis reduced to 1%):

$\begin{matrix}{\sigma = {\frac{3.912}{V}\left( \frac{\lambda_{550}}{\lambda} \right)^{q}}} & (62)\end{matrix}$where V is called visibility, λ₅₅₀, is the reference wavelength atλ=550, λ is the system laser wavelength, and q=q(V) is a power factor.(It should be noted that function: y=a^(x), where a<1, is amonotonically-decreasing function of x. Therefore, the λ-power factor inEq. (35) is monotonically-deceasing function of q.) Since, q-factor ismonotonically-decreasing function of V, therefore, the attenuationcoefficient, σ, is a faster decreasing function of V, than V⁻¹.

As an example, in a system where λ=1.6 μm:λ>550 nm  (63)The well-known phenomenological formula of dependence: q=q(V) has theform

$q = \left\{ \begin{matrix}{1.6,} & {{{for}\mspace{14mu} V} > {50\mspace{14mu}{km}}} \\{1.3,} & {{{for}\mspace{14mu} 6\mspace{14mu}{km}} < V < {50\mspace{14mu}{km}}} \\{{{0.16\mspace{14mu} V} + 0.34},} & {{{for}\mspace{14mu} 1\mspace{14mu}{km}} < V < {6\mspace{14mu}{km}}} \\{{V - 0.5},} & {{{for}\mspace{14mu} 0.5\mspace{14mu}{km}} < V < {1\mspace{14mu}{km}}} \\{0,} & {{{for}\mspace{14mu} V} < {0.5\mspace{14mu}{km}}}\end{matrix} \right.$The visibilities of equivalent atmospheric conditions are summarized inTable 3.

TABLE 3 Visibilities and Equivalent Atmospheric Conditions # AtmosphericConditions Visibilities 1. Exceptionally Clear V > 50 km 2. Very Clear20 km ≤ V ≤ 50 km 3. Clear 10 km ≤ V ≤ 20 km 4. Light Haze  4 km ≤ V ≤10 km 5. Haze 2 km ≤ V ≤ 4 km 6. Thin Fog 1 km ≤ V ≤ 2 km 7. Light Fog0.5 km ≤ V ≤ 1 km   8. Moderate Fog 0.1 km ≤ V ≤ 0.5 kmAccording to simulations, the atmospheric attenuation coefficientrelation:σ=σ(V,λ)  (65)includes both atmospheric absorption and atmospheric scattering, mostlyrepresented by so-called Mie scattering. This modeling should beunderstood in such a sense that only “ballistic” photons reachphotodetector array while both absorbed and scattered photons do notreach the receiver sub-system.

The attenuation coefficient value, 2σ, can be presented as a function ofvisibility, V, for specific wavelength, λ, in the look-up table form, asshown in Table 4, for λ=1.6 μm, in the visibility range; V=1 km-6 km.According to Table 3, it is equivalent to thin fog (1 km≤V≤2 km),through haze (2 km≤V≤4 km), and part of light haze (4 km≤V≤10 km).

TABLE 4a Look-Up Table for 2σ, Versus Visibility Range: 1-2 km V [km]1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 q 0.52 0.53 0.55 0.56 0.58 0.600.61 0.63 0.64 0.66 2σ [km⁻¹] 4.08 3.70 3.35 3.07 2.81 2.58 2.40 2.222.08 1.93

TABLE 4b Same as 2a, for V = 2-3 km V [km] 2.1 2.2 2.3 2.4 2.5 2.6 2.72.8 2.9 3.0 q 0.68 0.69 0.71 0.72 0.74 0.76 0.77 0.79 0.80 0.82 2σ 1.801.70 1.59 1.51 1.42 1.34 1.27 1.20 1.15 1.09

TABLE 4c Same as 2a, for V = 3-4 km V [km] 3.1 3.2 3.3 3.4 3.5 3.6 3.73.8 3.9 4.0 q 0.84 0.85 0.87 0.88 0.90 0.92 0.93 0.95 0.96 0.98 2σ[km⁻¹] 1.02 0.98 0.93 0.89 0.85 0.81 0.77 0.74 0.71 0.68

TABLE 4d Same as 2a, for V = 4-5 km V [km] 4.1 4.2 4.3 4.4 4.5 4.6 4.74.8 4.9 5.0 q 1.00 1.01 1.03 1.04 1.06 1.08 1.09 1.11 1.12 1.14 2σ[km⁻¹] 0.65 0.63 0.60 0.58 0.55 0.53 0.51 0.49 0.48 0.46

TABLE 4e Same as 2a, for V = 5-6 km V [km] 5.1 5.2 5.3 5.4 5.5 5.6 5.75.8 5.9 6.0 q 1.16 1.17 1.19 1.20 1.22 1.24 1.25 1.27 1.28 1.30 2σ[km⁻¹] 0.44 0.43 0.41 0.40 0.38 0.37 0.36 0.34 0.33 0.32

The system may handle the impact of visibility in various ways. Forexample, the step of obtaining voxels 1601 may comprise obtaining areduced set of voxels in lower visibilities. As another example, thestep of obtaining voxels 1601 may comprise angling the system to providea detection range (e.g. 402, FIG. 4B) that is closer to the system, sothat the entire available detection range (402) is visible.

Step 1601 may also include an automatic dynamic range adjustmentprocedure. For example, the system may adjust the pupil 1109 (ifpresent), activate a second detection system having a different dynamicrange, or activate a splitter 1110 (if present). If a second detector(from a second detection system or from a second detector 1103′) isused, the system builds the voxel space from the combined signals of thetwo detectors.

In step 1602, a clutter signal is obtained from the set of voxels. Forexample, in a system deployed on a ship mast, a clutter signal willoccur at the voxels corresponding to sea level. As described above,measured distance is a function of laser pulse return time and gatingspeed. FIG. 17B illustrates a “light line” of sea level clutter measuredbecause of this relationship. FIG. 17A illustrates the correspondingsystem geometry. The system 1748 is at a height h above sea level. Thesystem emits a laser pulse (including optical ray 1479) that reflectsoff of sea level clutter creating “light line” 1753, which manifests aplane of clutter signals in the three-dimensional set of voxels.

In step 1603, voxels are missing from the expected clutter signal aredetected. For example, in a clutter plane created by sea level, missingvoxels are created by objects (such as targets or other clutter objects)blocking the laser pulse and causing an early return pulse or byabsorbing the laser pulse, causing a late or non-existent return pulse.For example, in FIGS. 17A and B, the optical ray 1749 is not reflectedat sea level 1751, but rather at the sea clutter (sea wave) at point1750. At FIG. 17B, expected clutter at light line 1753 is broken inpoint 1754. As illustrated in FIG. 17B, all reflection points at the sealevel are located on light line with their z-coordinate on z-axis.However, because of light line symmetry breaking, the reflection point“moves” from point 1754 to point 1755, with z₁, z₂-coordinates shownboth in FIGS. 17 A and B, where (arrows 1756 and 1757 have equivalentinterpretation):Δz=z ₂ −z ₁  (66)

In FIG. 17B, projection of points 1754 and 1755 (or, their equivalents1750 and 1751 shown in FIG. 17A) on ct-axis is such that their distance,at ct-axis is 2Δz, while their distance at z-axis is only Δz, whichexplains 26.56°-angle value of line 1753, since tan 26.56°=0.5.

The light line symmetry breaking situation becomes more complex in thecase of other targets. For example, FIGS. 18A-C illustrate the situationof light line symmetry breaking in periscope detection. In FIG. 18A,three points A, B, C are shown, including the periscopic entrance/exitA; a low-brightness target at the periscopic surface B, (which acts as areference clutter reflecting object) and a clutter point C. Clutterpoint C is illustrated in FIG. 18B where optical ray 1860 passes pointC, reflecting at distant point 1861 (z₄-coordinate). Therefore, thisclutter object has the largest coordinate: ct₃, as 1862, with smallerct-coordinate 1863 for A-point, and smallest one 1864, for B-point.

For clutter point, C, the symmetry is not broken, because C-point islocated at light line 1865. The most broken light line symmetry is forlow-brightness point B, since, this breaking value is: 2Δz, whereΔz=z₂−z₁. High-brightness A-point has symmetry breaking less than2(z₃−z₁), because there is pulse time delay due to optical raypenetrating the periscope's interior. Assuming that the optical ray isreflected at the periscope and at its eye piece, this extra time delayis 2L, in ct-coordinates, where L is the periscope length. However, inthe case of reflection from intermediate retro-surface, with distance,L′, from periscope point A, this extra time delay will be 2L′, inct-coordinates, where L′<L, where L-periscope length.

The number of t-cell units: δz=(cδt)/2, this extra time-delay providesis as follows. For typical marine (mast) platforms (h=50 m), and typicalR-distances, (R=10 km), and for typical A-point height (H=3 m), the|z₃−z₁|-distance is about 600 m, and δz=1.5 m, for δt=10 nsec.Therefore, for periscope length; L=12 m:

$\begin{matrix}{{{\left( \frac{z_{3} - z_{1}}{\delta\; z} \right) = {\frac{600\mspace{14mu} m}{1.5\mspace{14mu} m} = 400}};{\frac{L}{\delta\; z} = {\frac{12\mspace{14mu} m}{1.5\mspace{14mu} m} = 8}};}{\frac{\left( {z_{3} - z_{1} - L} \right)}{\delta\; z} = 392}} & \left( {67{abc}} \right)\end{matrix}$Therefore, the value of periscope length in t-cell units is 8; i.e.,location of point A is separated by 8-number of t-cells (or, 8-number ofvoxels) from point, B. This is a significant value, which can be used asan extra temporal signature of periscopic target, even for single-pulsereflection.

The clutter point C is separated far from points A and B, in t-cellunits, since, according to Eq. (67a), for |z₄−z₁|≅|z₃−z₁|, we have about400-units separation. Therefore, the related clutter is separated quitefar from periscopic points' location, in t-cell units; thus, providingsignificant t-cell or, voxel or-units, separation. Accordingly, iftarget point, A, is located at (m+8)th voxel, for example, by using Eq.(39), the low-brightness periscopic point, B, is located at mth voxel,while C-point is located at (m+392)th voxel, according to Eq. (67).Therefore, the noise signals from reflective points, B and C, do notbias target signal from high-brightness point, A. In variousembodiments, targets may be detected using the t-cell separation ofsignals from background clutter signals as determined from the voxelreadouts.

Returning to FIG. 16, in step 1604, the voxel set is evaluated todetermine the location in voxel space of reflections causing the missingvoxels in the clutter signal. These voxels are identified as potentialtarget signals. The potential target signals may be located in front ofor behind their corresponding clutter signal (i.e., the target mayreflect rays that return prior to rays striking surrounding clutter orthe target may reflect rays that return after rays striking surroundingclutter). In some embodiments, this may comprise searching for thenearest voxel in or-units to a voxel missing from the clutter signal.

In other embodiments, step 1604 may comprise detect voxel coherencysignals. FIG. 19 illustrates voxel coherence in a vertical line ofvoxels. Typically, the pixel optical power of an image of integratedclutter, such as that of sea level, or Lambertian solid state (false)target such as a boat, a ship, a rock, is comparable with the opticalpower from strong non-Lambertian target such as retro-reflection from aperiscope. Such integrated clutter can be used as temporal reference forestablishing IOS voxel coherency, as shown in FIG. 19. This integratedclutter may be used as a temporal reference because the location ofLambertian objects and non-Lambertian target in voxel space are usuallylocated in different time-resolution voxel coordinates.

Vertical voxel coherency is illustrated in FIG. 19. A target comprisesperiscope 1900, with its entrance 1901, and its side 1902. The side 1902represents integrated Lambertian solid-state clutter working here as avoxel reference. Four (4) vertical pixels are considered for the sake ofexplanation, their object-inverse areas are 1903, 1904, 1905, and 1906(i.e., each pixel's vertical field of view (inverted)), respectively.Their voxel sets (derivatives) are represented by two exemplary columns1907 and 1908. Time coordinate 1909 illustrates that voxel column 1908occurs later on the time scale than column 1907 (i.e., voxels in column1908 measure signals that are farther than voxels in column 1907).Periscope 1900 total length is L 1910, while its frontal horizontallength is l 1911. For sake of simplicity, only one retro-reflection isassumed to occur from retroreflective surface 1912. Therefore, usingvertical line 1913, with its bottom point 1914, at sea level, the extratime delay for incident ray 1915 and its retroreflected ray 1916, is:2L=cΔt₁, where Δt₁ is total extra return-time for ray passing wholeperiscope interior, reflected from retro-surface 1912 and passingbackward through periscope interior. For laser pulse, with temporallength, δt, representing voxel length in light units, δz (where:δz=(0.5)cδt), this extra time delay Δt₁, is equal to the followingnumber of light units: N₁=L/δz. For example, for δz=1.5 m and L=12 m, weobtain: N₁=12/1.5=8. Using the same reasoning, the extra time delay forLambertian clutter 1902, is: N₂=l/δz. For example, for l=30 cm:N₂=0.3/1.5=0.2; i.e., practically the same time cell as without anyextra delay. Therefore, the retroreflected signal 1916 comes 8-lightunits (or 8 voxels columns in the δz direction) later than reflectedsignal 1917, while the general formula; is: ΔN=N₁−N₂=8−0.2≅8. The voxelcolumn 1907 represents extra-time delay for reflected ray 1917, whilethe voxel column 1908 represents extra-time delay for reflected ray1916. Thus, voxels 1918 and 1921 have signals, while voxels 1919, and1920 are empty. Similarly, for column 1908, only voxel 1922 has asignal.

The temporal relation between voxel columns 1907 and 1908 represents anexample of voxel coherency. By retrieving and analyzing all voxels fromthese columns, the system can identify two meaningful voxels 1918 and1922, representing the information about mutual location of tworeflected signals 1916 and 1917. In turn, the system can performreasoning about presence of periscope 1900, in respect to referenceclutter 1902. We see that this specific periscopic information can beobtained without using distinctive periscope optical signals, due toreference clutter 1902 which has comparable pixel signal power withhigh-brightness retro-reflected signal 1916.

Voxel coherency analysis may also be applied using all availabledimensions of the voxel space. FIG. 20 illustrates an example ofhorizontal voxel coherency. Indeed, in some embodiments, rather than atwo dimensional sensor array, a one dimensional sensor array is used.The one dimensional sensor array is arranged horizontally, in whichcase, only horizontal voxel coherency analysis is available.

FIG. 20 presents a case of horizontal voxel coherency involving aperiscope 2000, and retro-reflected beam from only one retroreflectivesurface 2001. Point A is at the periscope entrance with incident ray2002 and retroreflected ray 2003. In this figure, we consider threereflective objects A, B, C, representing: high brightnessretro-reflective object, A, reference solid clutter B, and the 2^(nd)reference sea clutter C, respectively. The slant of ray 2019, 2003, 2015has slant angle, β. β is shown, out of scale, because, in practice, forthe marine (mast) platforms, this slant is very small (β<<1). Threeexemplary voxel horizontal arrays, 2004, 2005, and 2006, are shown,representing the same horizontal pixel array, but different arrivaltimes: t₁, t₂, t₃ out of scale (i.e., difference between them is not thesame). Signal-filled voxels are 2007, 2008, 2009, 2011, and 2012, whileempty voxels are 2013, 2014, 2015, 2016, 2017, 2018, and 2010.

The incident ray 2013 strikes solid reference clutter 2014, and itsreflected ray is 2015. This reflected ray 2015 has the earliest arrivaltime, t₁, represented by voxel array 2004. The retro-reflected ray 2003has the second arrival time, t₂, represented by voxel array 2005. The3rd incident ray 2019 is reflected at sea point C, denoted as 2021, andincoming as reflected ray 2019, much later than other reflected rays2003 and 2015, at arrival time, t₃, represented as voxel array 2006. Thedistance between bottom point, B′, denoted as 2020 and C-reflectionpoint, 2021, is very large, say 600 m, for example. Therefore, fromgeneral formula: (t₃−t₂)=(2×600 m)/(3·10⁸ m/sec)=4.10⁻⁶ sec, while forspatial voxel quant of δz=1.5 m, this distance, in light units, is:(N₃−N₂)=(600 m)/(1.5 m)=400; i.e., very large, in comparison withperiscope return time for example (eight (8) light units); thus,(N₂−N₁)=8. Therefore, voxel arrays 2004 and 2005 are relatively close toeach other (N₂− N₁=8), while voxel arrays 2005 and 2006 are far away(N₃−N₂)=400.

The horizontal voxel coherency signature is represented by graphicalvoxel pattern of three horizontal voxel arrays 2004, 2005, and 2006, inrespect to signal-filled voxels and empty voxels. In particular,horizontal voxel array 2006 demonstrates a characteristic missing-toothpattern, with “missing” voxel (or “hole”) 2010, while this missing voxelis located at other voxel array 2005, at voxel 2008. The secondreference voxel is 2007, represents solid (hard) reference clutter B.This clutter plays a dual role, not only as regular clutter (a noise)but also as reference object, allowing the system to identify (ID)periscopic target 2000 as well us to find its location, with single timecell accuracy (˜1.5 m). This is done even without two-pulse operation.In further embodiments, the reference clutter may additionally oralternatively comprise the ground, clouds, or distant backgroundobjects.

In general, detectable targets will show significant space time voxelcoherency. FIGS. 21 A-D illustrate some general space-time voxelcoherency. All these clutter/target objects are represented by relatedvoxel intensity values:I=I(i,j,m)  (68)where; i, j, m—are integers, defining given voxel index; e.g.,I _(i,j,m) =I _(2,5,151) =I(2,5,151)=2.5·10⁻⁵ W/cm²  (69)where: i-index defines voxel's x-coordinate (horizontal); j-indexdefines voxel's y-coordinate (vertical); and, m-index defines voxel'sct-coordinate (in light units).

In FIGS. 21A-D, illustrations of space-time correlation between voxels'intensities, as defined by Eqs. (40-41), are shown. The location ofreflective point, B, has longitudinal coordinate, z=z₁, indexed by m=1,in FIG. 21A, where pixel fragment of 16-number of voxels, 2080, isshown, with exemplary ith-indexes: 7, 8, 9, 10, and jth-indexes: 5, 6,7, 8. In FIGS. 21B, 21C, and 21D, the voxels with the same i, j-indexes,but different m-indexes, are shown.

Returning to FIG. 21A, the lowest jth index: 5 represents sea level, atz=z₁, illustrated by three (3) wavy voxels 2101, including alsolow-brightness periscopic reference clutter (ie., the body of theperiscope), B, denoted as 2102, which covers two y-levels (˜5 m height).This is a kind of integrated clutter filling all pixel size, (forexample, for f=20 cm, R=10 km, the resolving element is about 2.5 m×2.5m), however, its optical power/intensity is medium-range, comparablewith integrated sea clutter intensity range. Therefore, both “wavy” and“horizontal” lines' voxel marks represent comparable medium-rangeintensity. In contrast, “empty” voxels, as 2103, represent low intensitylevels.

In FIG. 21B, the optical beam reflected from periscopic interior,represented by high-brightness target, A, is shown 2104, detected byvoxel with coordinates: (9, 7, 8). The voxel 2104, as representinghigh-brightness target, is marked by crossed double-diagonal lines. Now,voxels 2105 are empty, with low intensity levels (from only straylight); because, the beam was reflected earlier, detected by 2102voxels.

In FIG. 210, z=z₂ longitudinal coordinate is represented. Therefore, thebeam is reflected from integrated sea clutter (if, it is located at sealevel), represented by “wavy” voxels, 2106, while voxel, 2107, is empty,because the related beam has been detected by upper voxel, 2102 (withcoordinates: 9, 6, 1. Its m=200, assuming that target B's height is halfdistance of that of target A (i.e., equal to H/2).

In FIG. 21D, the integrated sea clutter at sea level, is reflected,represented by “wavy” voxels 2108, while voxel, 2109, is empty, becausethe related beam has been detected by pixel, 2104, in FIG. 21B.

In summary of FIGS. 21A-D, voxels such as 2101, 2102, 2104, 2105, 2106,2107, 2108, and 2109, are correlated by some space-time relation,representing certain anomalous event, namely, laser reflection off atarget (such as a periscope). Otherwise, all voxels with the followingj-coordinates:j=5, in FIG. 21A; j=6, in FIG. 21C, j=7, in FIG. 21D  (70)will be filled by light reflected from sea level, assuming sea clutterat sea level. The exception would be sea waves with amplitudes exceeding2.5 m (assuming exemplary conditions). These waves start to occupy somevoxel, with jth coordinates, higher than those in Eq. (42), such as j=6,in FIG. 21A; or j=7, in FIG. 210, for example. However, such waves wouldtypically not provide the voxel coherency signals associated withtargets.

In some implementations, the signal from high-brightness targets (suchas non-Lambertian reflectors) will tend to be smaller than the signalfrom surrounding clutter. This is because, although high-brightnesstargets reflect a greater amount of light per unit area back to thesystem, the clutter signal will be integrated over a much larger area.The system parameters may be set so that the upper range of the dynamicrange of the detector 1103 encompasses the expected signal from largearea clutter. In some embodiments, for example where some target signalsmay be greater than their reference clutter signals (for example, anocular target on a vessel with light absorbing paint), some systemparameters may be adjusted. For example, a pupil 1109 may be used toreduce the light gathering ability of the system to bring the targetsignal within the dynamic range of the detector.

In some embodiments, a second detection system may be employed inparallel. FIG. 110 illustrates such an embodiment. For example, a firstdetection system with a high light gathering ability may be used todetect low brightness signals while a second detection system may have areduced light gathering ability to detect high brightness signals.

Alternatively, a splitter 1110 may allow two detectors 1103, 1103′ anddetector electronics 1104, 1104′ to operate in parallel. One detector1103′ may be configured to detect higher brightness signals than theother 1103, for example by having larger sensor sizes or by having moresensitive sensors. In this case, each RISC 1108, 1108′ array 1104, 1104′provides its output to the detection processor 1105 and the detectionprocessor 1105 builds a combined voxel space from the two outputs.

In a further embodiment, the pupil 1109 is on only one branch of thedetection subsystem. FIG. 11D illustrates such an embodiment. Here,compared to FIG. 110, the pupil 1109 is after the splitter 1110.

In these embodiments, detectors 1103 and 1103′ may have different sensorsizes to accommodate the changes in light gathering ability introducedby the pupil 1109. As discussed herein, photodetectors 1103 and 1103′may be various types of detectors. For example, they may be APDs orsolid-state photomultipliers, satisfying performance conditions such assufficiently low NEP (preferably on the picowatt order), sufficientlyhigh speed (for example, greater than 100 MHz), and availability in anarray configuration (either one-dimensional or two-dimensional).

In still further embodiments, further photo detection branches may beemployed. For example, three or four photo detection branches may beemployed.

In other embodiments, for example, those using binary detection signalsinstead of multi-valued detection signals, high brightness signals areallowed to saturate the detector. Accordingly, the gain of the detectoris set for expected low signal levels, such as signals expected from lowreflective reference clutter objects, such as absorptive vessel bodies.

Returning to FIG. 16, in step 1605, bright voxels are detected. Brightvoxels are those voxels having a signal greater than clutter signal. Forexample, bright voxels may be defined as voxels having a signal somepredetermined amount more than a clutter signal. The clutter signalthreshold may be determined by averaging the clutter signals receivedduring the current voxel readout, or over some period of operating time.Bright voxels may be created by reflections from various targets. Forexample, bright voxels may be created by reflections off of one or moreretroreflective surfaces. For example, voxels 2104 from FIG. 21B, 2008from FIGS. 20, and 1922 from FIG. 19 may be bright voxels.

In step 1606, a reference voxel set (RVS) corresponding to the brightvoxel is detected from the voxel readout. The reference voxel setcomprises clutter signals from clutter surrounding the target (forexample, the clutter signals surrounding the missing voxels detected instep 1603). The reference voxel set may further comprise voxels nearbythe bright voxel that may be reflected by other parts of the target.Such other voxels will have signal levels commensurate with cluttersignals, but will be within some predetermined distance of the brightvoxels.

In step 1607, the reference voxel set and its relationship to the brightvoxel is analyzed for target detection. For example, in one embodimentthe distance between the bright voxel and all or a portion of thereference voxel set is determined. For example, in FIGS. 21A-D thedistance between missing voxel 2102 and its gap 2107, is significant andequal to Δm=200−1=199, while, in the case of typical sea waves, suchdistances will be rather small (because, their heights are rathersmaller). Based on the analysis, targets may be detected and identified.For example, periscopes or other ocular devices may be detected.

In some implementations, various truthing experiments may be performedto determine a figure of merit (FoM) necessary for step 1607 to detectand identify a target. An example of such an analysis would be opticalperiscope detection, against sea clutter and other false targets. TheFoM may be developed pursuant to probability of false alarm (PFA), falsealarm rate (FAR), false positives, false negatives, and otherconsiderations. The FoM may be developed using a statistical analysis,based on Bayesian inference (BI). For example, various mock-ups ofdifferent target types and different reference clutter types (such asdifferent periscopes on different submarines) may be used to determineappropriate reference clutter and target signals. In particular, thesetruthing experiments may be used to maximize the PPV of the system.

For the sake of explanation and to simplify Bayesian inference (BI), twobinary events are considered: signal, or true target; and, noise(clutter), or false target. The event of detection of a signal isdenoted S; and, the sensor readout corresponding to the event as S′.Similarly N (event) and N′ (sensor readout) will denote noise. Then, twoabsolute probabilities: p(S), and p(N), mean probability of signal andnoise, respectively, with conservation relation:p(S)+p(N)=1  (71)because there are only two exclusive events. There are four conditional(direct) probabilities:p(S′|S)−probability of detection (PoD)  (72a)p(N′|N)−probability of rejection (PoR)  (72b)p(S′|N)−probability of false positives  (77c)p(N′|S)−probability of false negatives  (77d)For example, p(S′|S) means the probability, that, under signal event,sensor readout will also show signal. Also, p(S′|N) is probability thatpositive readout (S) is false (since event is noise). Therefore, it canbe also called probability of false alarm (PFA); or, the false alarmrate (FAR).

In the case of the BI, inverse conditional probabilities can bemathematically derived from the absolute and direct conditionalprobabilities. For example, positive predictive value (PPV) is: p(S|S′);i.e., probability of signal event, assuming, that signal readout didoccur. According to the Bayesian paradox:(PPV)=p(S|S′)  (78a)(PPV)<(PoD)  (78b)The PPV figure is defined as (assuming large number of samples):

$\begin{matrix}{{PPV} = \frac{{Number}\mspace{14mu}{of}\mspace{14mu}{True}\mspace{14mu}{Alarms}}{{Number}\mspace{14mu}{of}\mspace{14mu}{All}\mspace{14mu}{Alarms}}} & (79)\end{matrix}$Therefore, the PPV may be utilized as a FoM for periscopic targettruthing (or experimental validation) experiments; i.e., for testing asystem while simulating (or, real) true targets (periscopes) and falsetargets (oculars, small boats, sea clutter, etc.) and with possibleincreasing P(S) to higher values than in likely real-world scenarios(for training purposes).

In general, it is desirable to minimize p(S′|N) and p(N′|S) whilemaximizing PPV. Additionally, as false negatives represent missedtargets, it is desirable to obtain a very low amount of false negatives.This can be done independently of PoD by minimizing false positive withrespect to p(S): p(S′|N)<p(S).

FIG. 22 illustrates a method of target detection discrimination forperiscopes through inference. In typical environments where periscopes2205 are present, various clutter objects may also be present. Forexample, sea spikes, breaking waves, and other natural water formations2201, and small boats and other moving objects 2202, rocks and otherstationary objects 2203 may be present in the environment. Additionally,objects such as monoculars or other ocular devices 2204 (e.g., an OAD901 (FIG. 9)) may have some similar characteristics to periscope 2205that would make them difficult to discriminate from periscopes 2205.

In step 2206, sensor readouts are evaluated to detect a retroreflectiveeffect to discriminate non-ocular clutter 2207 from ocular potentialtargets 2208. Retroreflection occurs when a refracting optical elementand a reflective surface are arranged so that the focal surface of therefractive element coincides with the reflective surface. Opticalsystems, such as periscopes, binoculars, cameras, monoculars, otheroptical devices, and eyes, often exhibit retroreflection, at least forincident rays within the field of view of the optical system. The lightreflected from a retroreflectors is reflected back to its source withlittle divergence or no divergence. In some cases, the light reflectedback from a retroreflector may have a beam divergence of 0.25° or less.However, in other cases, the light reflected back from a retroreflectormay have a greater beam divergence. Accordingly, the retroreflectedsignal from ocular potential targets 2208 will be greater than thenon-ocular clutter 2207, which typically exhibit Lambertian,near-Lambertian, or other divergent scattering. Accordingly, for voxelsaway from the clutter plane caused by sea level, signal strength may beused to discriminate between non-ocular clutter 2207 and ocularpotential targets 2208. Any signals from non-ocular clutter 2207 may berejected 2212. In some embodiments, the voxel readouts include measuredsignal strength. In other embodiments, the voxel readouts are binary,with a signal detected if measured signal strength is above a threshold.This threshold may be set to a value likely to exclude non-ocularclutter 2207 from ocular potential targets 2208.

Omnipulse discrimination 2210 may be used to distinguish between ocularclutter 2209 (such as optical device 2204) and periscope targets 2211.Omnipulse discrimination 2210 refers to using the tendency of aperiscope to produce multiple retroreflective return signals for targetdiscrimination. FIG. 23 illustrates this method. The omnipulse method isillustrated for two return-pulses, for simplicity. Assuming laser pulsetemporal length, δt, and its spatial length, δl, we have:δt=cδt  (80)For example, for δt=10 nsec, δl=3 m, but for δt=1 nsec, δl=30 cm.

In FIG. 23, the incident laser pulse, 2300, is incident at theentrance/exit of perioscope, 2301, penetrating perioscope interior,2302. Then, it is reflected from the 1^(st) retro-surface (which is anyfocal plane), such as reticle (2a), 2303; then, passing ΔL-distance(with L-periscope length), and reflecting from the 2^(nd) retro-surface,such as eye piece, (3a), 2304. As a result, two return pulses, 2305 and2306 occur. More than two retroreflective return pulses may occur,including pulses for all possible (relay) focal planes. Such surfaces donot need to have central reflection interface, since, vignettingretro-reflection may occur (reflections from boundaries is sufficient.)In order to obtain the pulse separation, the following condition has tobe satisfied:

$\begin{matrix}{{{2\Delta\; L} > {c\;\delta\; t}};{{\Delta\; L} > \frac{c\;\delta\; t}{2}}} & (81)\end{matrix}$

For example, for δt=10 nsec, Eq. (81) yields: ΔL>1.5 m; but, for δt=1nsec, ΔL>15 cm. Therefore by reducing laser pulse temporal length, δt,can increase the omnipulse resolution, since, for δt=1 nsec, theseparation between two retro-surfaces must be larger than only 15 cm.Eq. (81) can be generalized for a number of retro-surfaces larger thantwo; assuming condition (81) satisfied for any two sequentretro-surfaces.

Returning to FIG. 22, omnipulse discrimination 2210 may be used todistinguish and reject 2213 ocular clutter 2209 from periscopic targets2211, which cause the occurrence of a detection event 2214. An omnipulsesignature is typically characterized by multiple return pulses from asingle x,y, location but with different return pulse times (and hence,different z locations in the voxel readout). In one embodiment,omnipulse signatures may be determined for various different periscopetypes. These omnipulse signatures may be detected in the voxel readoutsand used for target identification. In another embodiment, any readinghave the characteriscs of an omnipulse is viewed as a potential target.Various other inferential rules, such as use of reference integratedclutter may then be applied to distinguish between a false positive andtrue positive.

Returning to FIG. 16, in some implementations step 1601 comprisesobtaining multiple voxel readouts from different times. This allowsdetection of changes in the detection zone. When multiple time indexedvoxel readouts are accumulated, the resultant space may be indexed usingfour dimensions. The set of four-tuple indexed voxels obtained frommultiple readouts from the modules field of view is termed the set of 4Dvoxels, or hypervoxels. The set of hypervoxels may be obtained bysending next PFF (Pulse Facet Flash), and observe state change from onetime moment, t₁, to other time moment, t₂, where:Δt=t ₂ −t ₁ ;t ₂ >t ₁  (82)Where, Δt is time difference between those moments. Furthermore,multiple PFFs, in time moments: t₁, t₂, t₃, etc, (either periodically,or not) may be sent to build as large a hypervoxel space as desired. Forsimplicity of explanation, it is assumed that PFFs are sentperiodically. However, the non-periodic case is a straightforwardextension In the periodic case:Δt=t ₂ −t ₁ =t ₃ −t ₂ =t ₄ −t ₃= . . .   (83)Previously, three voxel indices were employed: i, j, m, related to(x,y,z)—coordinates, respectively. Now, four voxel indices are relatedto four voxel coordinates: (x, y, z, t), in the form:(x,y,z,t)⇒(i,j,m,k)  (84)where index, k, where k=1, 2, 3, . . . , is related to new timecoordinate, t, related to different PFFs, obtained from different timemoments: t₁, t₂, t₃, etc.

Therefore, in the case of voxel change detection, Voxel Change Coherency(VCC) may be employed in the method. Voxel change coherence isdetermined in four-dimensional (4D) space (x, y, z, t), defined by Eq.(84), which is a kind of hyperspace.

The 4D voxels, or hypervoxels, are: elements, quants, or units of 4Dspace (x, y, z, y), characterizing voxel change coherency (VCC), in theform of indexing: (i, j, m, k), as described in Eq. (82-84). In thiscase, (x,y)-arc lateral pixel coordinates, z—is longitudinal voxelcoordinate, and t—is (independent) time coordinate. In fact, there aretwo time coordinates: t, and t′, the latter one being dependent(connected) time coordinate, connected with z-coordinate, by relation:2z=ct′ (t′-coordinate has, previously, been denoted by t). The sub-setof 4D hyperspace: (x, y, z, t) is called cross-section, and can beitself 3D space, or 2D space. Any subset of 4D space: (x, y, z, t), withconstant one coordinate (such, as t, for example), is 3D spacecross-section. The 3D voxels discussed above are related to 3D spacecross-section: (x, y, z, t_(O)), in the form:(x,y,z,t)/t=t _(o)=CONSTANT  (85)i.e., for single, PFF (Pulse Facet Flash). Then, 4D hypervoxels arereduced to 3D voxels, quantizing space: (x,y,z).

In kinematics, the general movement of material point (a point object)is described by three (3) equations in 4D space (x, y, z, t), in theform:x=x(t),y=y(t),z=z(t)  (86abc)and, the momentary (instant) speed (velocity) vector, is

$\begin{matrix}{{\overset{\rightarrow}{v} = {\lim\limits_{{\Delta\; t}\;->0}\frac{\Delta\;\overset{\rightarrow}{r}}{\Delta\; t}}};{\overset{\rightarrow}{r} = {\overset{\rightarrow}{r}\left( {x,y,z} \right)}}} & \left( {87{ab}} \right)\end{matrix}$where: {right arrow over (r)}={right arrow over (r)}(x,y,z) isdirectional vector. Parametrically, the movement:{right arrow over (r)}={right arrow over (r)}(t)  (88)where {right arrow over (r)} is directional vector, {right arrow over(v)}—its instant speed, and (x,y,z)—are its coordinates as functions oftime, t. In the VCC case, this movement is described by four discretecoordinates: (x, y, z, t), indexed by: (i, j, k, m). Then, instead ofmomentary (instant) vector, {right arrow over (v)}, there is an almostmomentary, or momentary-mean (MM) vector, {right arrow over (v)}′,which, further, will be denoted as, simply, {right arrow over (v)}′, inthe form of ratio of Δ{right arrow over (r)} and Δt:

$\begin{matrix}{{\left. {\overset{\rightarrow}{v}}^{\prime}\Rightarrow\overset{\rightarrow}{v} \right. = \frac{\Delta\;\overset{\rightarrow}{r}}{\Delta\; t}};{{\Delta\;\overset{\rightarrow}{r}} = \left( {{\Delta\; x},{\Delta\; y},{\Delta\; z}} \right)}} & \left( {89{ab}} \right)\end{matrix}$where, arrow shows changing of symbolics: from {right arrow over (v)}′to {right arrow over (v)}.

The 4D resolution of material point movement, described by MM-velocityvector, {right arrow over (v)}, is characterized by pixel sizes: a_(x),a_(y), δz—longitudinal resolution, and time coordinate change, Δt.

In the lateral movement case, described by (x,y)-coordinate, and theirindices: (i,j), the lateral resolving elements: δ_(x), and δ_(y), arederived from the following relations:a _(x) =m _(x) δx;a=m _(y) δy  (90ab))where: m_(x), m_(y) is x, y—IOS system magnification, or, ratherde-magnification, because: m_(x)<<1, and m_(y)<<1.

In the longitudinal movement case, described by z-coordinate, thelongitudinal resolving element, δz, isδz=(0.5)cδt _(B)  (91)where: δt_(B)=B⁻¹, and, in ideal case: δt_(B)=δt_(L), whereB—photodetector bandwidth, and δt_(L)—laser pulse temporal length.

The time resolving element, Δt, is defined by Eq. (82). In summary, 4Dresolution of 3D movement in hypervoxel space: (x, y, z, t), which istime-space, is defined by lateral, longitudinal, and time resolvingelements:(δx,δy,δz,Δt).  (92)Therefore, MM-velocity vector resolution is also described by these four(4) resolving elements.

When hypervoxels are introduced in step 1601, the analysis may compriseanalyzing movement in the hypervoxel space. FIGS. 24-26 illustrateexamples of movement in hypervoxel space.

The term foxel refers to a signal-filled voxel, while the empty voxel,“left” by this foxel, will be called a hole, resulting in foxel-holepair. When the dynamic cases in time-space (x, y, z, t), foxel-hole pairmovement (FH-Pair movement) will occur. Such FH-Pair movement can beeither rigid, or elastic. In the 1^(st) (rigid, solid state) case, thedistance between foxel and hole remains constant at a time, t, while inthe 2^(nd) (elastic) case, this distance changes with time. FIG. 24illustrates an example of rigid foxel group movement. Here, the 3Dcross-section-set (CSS) is illustrated, for m=m_(O)=constant, andvariable k-index for four k-values: k=1, 2, 3, 4.

Here, foxels 2400, 2401, and 2402 move rigidly. At t=t₁, these foxelshave the following pixel (x,y)-locations: for 2400 (i=3, j=4); for 2401(i=3, j=3); for 2402 (i=4, j=3). At t=t₂, these (i,j)-locations are:(2,4), (2,3), and (3,3)—respectively. At t=t₃, (or, k=3), the locationsare: (1,4), (1,3), and (2,3). At t=t₄ (k=4), the locations are: (3,2),(3,1), and (4,1). Therefore, for this foxel rigid group, t first, i.e.,for t₁≤t≤t₃, the lateral movement from right to left, along x-coordinatewhich is decreasing, with the following MM-velocity vector:

$\begin{matrix}{{\overset{\rightarrow}{v} = {\overset{\rightarrow}{v}\left( {{v_{x}0},0} \right)}};{v_{x} = {- \frac{\delta\; x}{\Delta\; t}}};{{\Delta\; t} = {{t_{2} - t_{1}} = {t_{3} - t_{2}}}}} & \left( {93{abc}} \right)\end{matrix}$where: δx=a_(x)/m_(x), where a_(x) is x-pixel size, and m_(x) issystem-de-magnification (m_(x)<<1). It should be emphasized that, inthis particular PFF (Pulse Facet Flash) case, the absolute distance, z,from an object to platform is known (by measuring beam return time). Forexample, for z=1 km, and f=50 cm (focal length), we obtain: m_(x) ⁻¹=(1km)/(50 cm)=1000/0.5=2000, and m_(x)=1/2000=5·10⁻⁴. Then, for a_(x)=20μm, for example: δx=a_(x)m_(x) ⁻¹=(2000) (20 μm)=(2000) (20·10⁻⁴ cm)=4cm; i.e., x-resolving element size is 4 cm. Then, for Δt=0.1 sec. forexample:|v _(x) |=v=(4 cm)/(0.1) sec=40 cm/sec.  (94)Therefore, by this kind of “forensic” analysis, the system can determinean approximate speed of a given group of foxels: 2400, 2401, 2402. Thisfoxel group represents some object with “L”-profile, as with sizes:L_(x), L_(y), where L_(x)=L_(y)=L, and L=2δx=8 cm. At t=t₄ (k=4), thisfoxel group suddenly move to the right-bottom corner. Therefore, fort₃≤t≤t₄, its MM-velocity vector, {right arrow over (v)}, is

$\begin{matrix}{{{\overset{\rightarrow}{v} = \left( {v_{x},v_{y},0} \right)};{v_{x} = \frac{\Delta\; x}{\Delta\; t}}},{{v_{y} = \frac{\Delta\; y}{\Delta\; t}};{{\Delta\; t} = {t_{4} - t_{3}}}}} & \left( {95{abcd}} \right)\end{matrix}$where Δx=3δx=12 cm, Δy=−|Δy|=−12 cm, and,

$\begin{matrix}{v = \frac{\sqrt{\left( {\Delta\; x} \right)^{2} + \left( {\Delta\; y} \right)^{2}}}{\Delta\; t}} & (96)\end{matrix}$

For example, for Δt=0.1 sec: v=(17 cm/0.1 sec=1.7 m/sec. In summary, atfirst, this L-object moves with 40 cm/sec-speed into opposite x-axisdirection, and then, it moves, diagonally, into “south-east,” withhigher 1.7 m/sec-speed. Additionally, a 2^(nd) group of foxels: 2003,2004, and 2005, which arrived at t−t₁ (k=1), and then, disappear fromthis set of voxels. Then, the system would search this group in othersets of voxels. Accordingly, during the analysis step, various foxelgroups may be identified and tracked. Their movement patterns may beused for target identification.

FIG. 25 illustrates an example of rigid foxel-hole pair movement in adifferent projection of the hypervoxel space in two dimensions. Thisfigure represents the rigid foxel-hole (FH)-pair that moves,longitudinally, with Δm=9 (between m=101 and m=110, for example), andΔk=2 (from k=2, to k=4). Assuming that: Δt=t₄−t₂=1 sec, for example, andδz=10 cm: Δz=Δmδz=(9)(10 cm)=90 cm; thus, the longitudinal speed of thispair is: 90 cm/sec. The FH-pair is rigid, because, a longitudinaldistance between foxel 2510, and its “hole” 2511 is constant (Δm′=4,between m=105 and m=101, or, between m=114 and m=110). Also, theintegrated clutter (RIC), marked by foxels: 2512, 2513, and 2514, is atthe constant distance from foxel 2510, confirming that the FH-pair isrigid, indeed.

FIG. 26 illustrates an example of non-rigid Foxel-Hole (FH) Pairmovement, FIG. 26 includes two diagonal columns, indexed by k=1, andk=2, respectively. The (identical) 2D-cross-sections of lateral(x,y)-pixels are only shown (six of them), with indices: i=5, 6, 7, 8;and j=11, 12, 13, 14. The 1^(st) diagonal column (k=1) is represented bythree (3) 2D lateral cross-section-sets (CSS), indexed by m=10, 12, and20. The same m-indices (10, 12, 20) are representing the 2^(nd) column(k=2). Of course, k=1 represents earlier time than k=2, as illustratedby the direction of t-axis. The foxel-group of four (4) foxels, markedby: 2620, 2621, 2622, 2623, is moving through the following (i, j, m,k)—transformation; related to foxels: 2620, 2621, 2622, 2623:

$\begin{matrix}{\left\{ {i,j,m,k} \right\}:\left. \begin{matrix}\begin{Bmatrix}{6,12,10,1} \\{7,12,10,1} \\{6,11,10,1} \\{7,11,10,1}\end{Bmatrix} \\{{{Column}\mspace{14mu} k} = 1}\end{matrix}\Rightarrow\begin{matrix}\begin{Bmatrix}{7,13,12,2} \\{8,13,12,2} \\{7,12,12,2} \\{8,12,12,2}\end{Bmatrix} \\{{{Column}\mspace{14mu} k} = 2}\end{matrix} \right.} & (97)\end{matrix}$The hole-group of four (4) holes, marked by: 2624, 2625, 2626, 2627, ismoving through the following (i, j, m, k)—transformation:

$\begin{matrix}{\left\{ {i,j,m,k} \right\}:\left. \begin{matrix}\begin{Bmatrix}{6,12,20,1} \\{7,12,20,1} \\{6,11,20,1} \\{7,11,20,1}\end{Bmatrix} \\{{{Column}\mspace{14mu} k} = 1}\end{matrix}\Rightarrow\begin{matrix}\begin{Bmatrix}{7,13,20,2} \\{8,13,20,2} \\{7,12,20,2} \\{8,12,20,2}\end{Bmatrix} \\{{{Column}\mspace{14mu} k} = 2}\end{matrix} \right.} & (98)\end{matrix}$

Comparing Eq. (97) and (98), both foxels and holes have the same lateral(i,j)-indices for both columns: k=1 and k=2. For example, for the 1^(st)column (k=1), the foxel 2620, and its hole 2624, have the same indices:(6, 12); the same with k=2, where this FH-pair has indices (7, 13).However, their longitudinal m-indices are different: 10 vs. 20, for the1^(st) column, and 12 vs. 20, for the 2^(nd) column.

Therefore, this FH-pair is elastic one. Also, crossed voxels (foxels) in2D CSS, denoted by k=1 and m=20, as well as in 2D CSS, with k=2, m=20,represent the RIC (Reference Integrated Clutter), because, their m-indexdoes not change (m=20=constant). In contrast, the foxels in 2D CSS,represented by (m, k)=(10, 1), and (m, k)=(12, 2), do change theirlongitudinal position. Thus, they represent a moving object, while theRIC represents only its (moving) (x,y)-projection. Accordingly, systemsmay detect reference clutter signals (e.g., perform step 1602 of FIG.16) by performing hypervoxel analyses.

The moment of the object represented by foxels: 2620, 2621, 2622, 2623,has an MM-velocity vector, {right arrow over (v)}, with all threenon-zero coordinates: {right arrow over (v)}′=(v_(x), v_(y), v_(z)). Forexample, for Δt-representing time difference from k=1 to k=2, equal to:Δt=1 sec, and for lateral resolving element: δx=δy=10 cm, its x-movementis represented by Δi=1, only (e.g., from i=6, to i=7). Therefore:

$\begin{matrix}{v_{x} = {\frac{\Delta\; x}{\Delta\; t} = {\frac{\delta\; x}{\Delta\; t} = {10\mspace{14mu}{{cm}/\sec}}}}} & (99)\end{matrix}$Same with y-movement (Δj=1); thus, also:v _(y) =v _(x)=10 cm/sec  (100)In order to estimate its longitudinal movement, Δm=2 (from m=10, tom=12). Thus, according to the orientation of right-hand(x,y,z)-coordinate system its:Δz=−2δz  (101)and, for δz=20 cm, for example:v _(z)=−20 cm/sec  (102)Accordingly its velocity vector is:{right arrow over (v)}=(10 cm/sec,10 cm/sec,−20 cm/sec)  (103)

The object with size (2δx, 2δy) has a velocity vector, described by Eq.(103). Its movement is represented by (i, j, m, k)—discrete coordinates(indices) through transformation from column (k=1) table to column (k=2)table, as in Eq. (97), while its lateral (x,y)-projection, representedby RIC (Reference Integrated Clutter), moves through transformation oftables in Eq. (98). However, the specific MM-velocity vector values canbe found only when the 4D resolution is known, represented by four (4)resolving elements: δx, δy, δz, and Δt.

In some implementations, the hypervoxel analysis may be used to performdetection without the use of reference clutter signals.

An example of a detection and analysis method is described withreference to FIG. 27. For sake of TOI extraction from RIC, the systemperforms a technique based on use of a RISC processor array, assuminghyper-voxel 4D space, by voxel-by-voxel 3D frame comparison(subtraction) at two different times t₁ and t₂. Additionally, the RISCarray may perform a 3D frame virtual translation by shift register. The1^(st) operation is for 3D velocity flow mapping, while the 2^(nd)operation is for the COI contour extraction. Both operations arepossible, however, only the 1^(st) operation is discussed here, forsimplicity.

As an example, a 100×100 photodetector array, per facet; thus, for100-facets per second, the frame has: 100×100×100=10⁶-pixels.Additionally, with gating there is also signal return z-coordinate.Assume long-range IOS geometry, as in FIGS. 3 and 4. Then, for typicalfacet angular acceptance of 0.4°-per facet, and marine platform with 50m—mast, and R=10 km—nominal distance, vertical coverage is of distancesbetween R=5 km and R=15 km. Therefore, for single facet, the 1^(st)pulse arrives from R=5 km distance, and the last one from R=15 kmdistance. Assuming laser pulse length, τ_(L)=10 nsec=10⁻⁸ sec, theaverage number of temporal cells, N_(t), is

$\begin{matrix}{N_{t} = {\frac{\Delta\; R}{c \cdot \tau_{L}} = {\frac{10\mspace{14mu}{km}}{\left( {{3 \cdot 10^{5}}\mspace{14mu}{{km}/\sec}} \right)\left( {10^{- 8}\mspace{14mu}\sec} \right)} = {{\left( \frac{1}{3} \right)\left( 10^{- 4} \right)\left( 10^{8} \right)} \cong 3000}}}} & (104)\end{matrix}$Then, the total number of parallel voxels, isn _(3D)=(10⁶)(3·10³)=3·10⁹  (105)

Using a 200 MHz-speed 256-RISC processor array, with total RISCoperation time of 4 msec per 8.3 Mb-parallel pixels as an example, for3·10⁹-number of parallel calculations, this time, t_(RISC), is

$\begin{matrix}{t_{RISC}^{\prime} = {{\left( {4\mspace{14mu} m\mspace{14mu}\sec} \right)\left( \frac{3 \cdot 10^{9}}{8.3 \cdot 10^{6}} \right)} = {{\left( \frac{12}{8.3} \right)\sec} = {1.45\mspace{14mu}{\sec.}}}}} & (106)\end{matrix}$

In this method, further the system identifies all COIs, by using virtual3D frame shift. Then, the system attaches a velocity vector to each COI,by using voxel-by-voxel comparison, and Euclidean distance computing,using RISC processor array. Then, Cluster Voxel Velocity (CV2) flowmapping, or CV2-flow mapping, may be obtained as in FIG. 27.

In FIG. 27 a portion 2730 of a cluster voxel velocity (CV2) flowmapping, or, shortly, CV2-flow mapping of COIs is illustrated, bycomparing two 3D voxel frames, at times t₁ and t₂, in (x,y,z)-coordinatesystem 2731; i.e., this illustration is in 3D, not in 2D. In thisexample, one velocity vector 2732 is longer than another one 2733. Thisis because the vector module 2732 is larger than vector value 2733. Thedot 2734 denotes the COI-location. By using more such time-comparisons:t₂ vs. t₁, t₃ vs. t₂, etc., and using the velocity formulas, the systemcan determine and analyze the kinematics of these clusters; and, then,make recognition between TOIs and RICs. For the velocities of sea wavespikes, at littoral waters, for example, they are rather random in valueand direction, in contrast to those of ships which are rather regular,in both value and direction. Also, such static RICs as rocks, forexample, will have zero-velocities. Accordingly, this movement may beused as an additional signature for distinction between TOIs and RICs.

The system and methods detailed above can be applied to otherapplications then those reflected to marine augmented target with highbrightness in retro-reflection. In other words, those targets do notneed to be reflective non-Lambertian (RNL) ones only, especially whenshorter distances are included. Also, since the VC is based on generalintegrated reference reflection clutter (IRRC), the IRRC does not needto be sea waves, but, also flat, or folded ground, for example.

One such application is the detection of a tripwire above ground. Insuch a case, such low-contrast (e.g., plastic) trip-wire can be almostinvisible to human eye. In this case, the reference clutter signal canresult from the ground behind such a wire, as shown in FIG. 28. In thisfigure, the pulse facet flash (PFF) detection of such trip-wire isshown, using the ground level as IRRC, for example. The PFF verticalcross-section is marked by crossed-area 2800. The PFF is illuminatingsome ground region, 2801, shown as flat one, for simplicity, and theincident rays, 2802, 2803, 2804, and 2805, are reflected (returned) atsome points such as A′, B′, C′, and D′, where points A′, C′, and D′ arelocated on the ground, while point B is the point located above theground, possibly a target. If this target is the wire cross-section,with wire direction perpendicular the figure; then it is single-point,B, marked as 2806. Otherwise, at skew position, the wire will berepresented by some line. The broken line 2807 shows that there is noconnection, at this point, between point B, and its ground projection,B′.

In order to explain some quantitative parameter values, a referencegeometry is introduced, assuming, for example, OA′=50 m, and OD′=100 m.In order to calculate, unknown B′C-distance, as an example: h=3 m, andBB′=20 cm (marked by 2807). Then, the unknown B′C-value, denoted as, w,can be estimated from the following trigonometric similarly relation:

$\begin{matrix}{{\frac{h}{{OC}^{\prime}} = \frac{{BB}^{\prime}}{B^{\prime}C^{\prime}}};{{OC}^{\prime} = {{OB}^{\prime} + {B^{\prime}C^{\prime}}}}} & (107)\end{matrix}$Assuming typical BB′-value of 10 cm, Eq. (72) becomes (w=B′C):

$\begin{matrix}{\frac{h}{{OB}^{\prime} + w} = \frac{{BB}^{\prime}}{w}} & (108)\end{matrix}$Solving this equation, in respect to unknown: w-value, where: h=3 m,BB′=10 cm, OB′=70 m (so, A′B′=20 m): w=B′C′=2.4 m.

In order to identify target, B, as a wire, however, vertical voxelcoherency (VVC) is used. Still further confirmation will be provided byhorizontal voxel coherency (HVC). Therefore, the 2D photodetector pixelarray (or, 2D PPA) is preferable. 2D PPA with moderate 60×40-pixelresolution is assumed for sake of simplicity of explanation. First,horizontal pixel resolution for single facet, with typical narrow FOV=3°is estimated. Then, at 100 m-distance, the horizontal range is about10.5 m; thus, horizontal object resolving element is: (105 cm)/(60)=1.75cm. For simplicity, vertical angular size of the PPF is assumed to besimilar to that of horizontal; i.e., 413=6°, marked as 2808.

Another example of system generalization is the changes in soil density.Changes in density in highly-porous soils (e.g., highly-humid, or poorlysettled dirt) that be partially penetrated by high pulse-power IR-beammay be detected. Assuming: 10 MW-pulse optical power andsuper-high-sensitivity of photodetector array, with noise equivalentpower of 0.1 pW, for example, extremely high detection dynamic range of10⁷/10⁻¹³=10²⁰=200 dB is obtained. In this application, voxel temporalresolution is also high, with δz=100 μm=0.1 mm, for example. Then, laserpulse temporal length, δt, must be 0.67 psec obtained from relation:δz=(0.5)c·δt, or 0.67·10⁻¹² sec. In such a case, from voxel distance,the soil penetration profile:z=z(x,y)  (109)The profile varies with internal structure, modified by, perhapsman-made modification, either by introducing more humidity, or bydigging in ground. The profile; z=z(x,y), is obtained from photodetectorpixel structure, while longitudinal resolution is defined by δz-valuewhich is proportional to laser pulse length, δt.

A third additional application is the detection of finger-prints. Theapplied laser pulse beam has a pulse length, δt, and equivalentlongitudinal resolution, δz, defined by relation: δz=(0.5)cδt.Additionally, eye-safe infrared beams may be used with wavelengths ofgreater than 1.3 or 1.5 μm. In FIGS. 29A-B, the finger papillary linesare shown, marked as 2920, and the finger-print cross-section profile2921, is shown in including the PFF, 2922, represented by incident rays2923, 2924, 2925, 2926 and their reflected rays 2927, 2928. If the laserpulse longitudinal resolution, δz, or 2929 is sufficiently high, thereflected rays 2927 and 2928 will belong to different voxels. In suchcase, if also vertical pixel resolution, δy, or 2930, is sufficientlyhigh then three dimensional (x,y,z)-mapping of finger prints, such as(x,y), or 2931 is obtained. As a result, by using standard software, wecan obtain the finger print profile, where z-axis is marked as 2932,while (x,y)-mapping is marked as 2931. Then, by using the secondstandard finger-print software, we can find all characteristic fiducialmarkings, such as 2933, for example, and, as a result, reconstruct wholefinger characteristic.

Since, for typical finger print profile sizes, δz ˜200-400 μm, and δy˜300 μm, the system comprises a pixel array zoomed on finger-region.Thus, for typical rather small pixel-numbers, for such long wavelengths(˜1.5 μm), in the range: 60×40, for example, the system employs a secondstandard camera, in order to find region of interest (ROI), which ishuman hand with visible finger prints, we need to either manually, orautomatically, find the ROI. In the latter case, the system applies somestandard pattern recognition algorithm.

A further application may be the detection of objects under the ground.Here, the system applies soil profilimetry in connection with detectionof trip wires described with respect to FIG. 28.

As described above, various application time gate the sensor to providevoxel readouts. In some embodiments, the time gating may be performed ata faster rate to sample the reflected laser pulses. This may be used toprovide pulse partition voxel coherency (PPVC), related to laser pulsepartition/sampling as shown in FIGS. 30A-B. The laser pulse 3000, withpulse temporal length, (δt)_(L), is sampled, with sampling constant(δt)_(B), and temporal samples 3001 (crossed area). As a result, thecontinuous instant power, P, line 3002, is replaced by discrete,“stairs”—line 3003, characterized by Momentary/Mean-power, {right arrowover (P)}, 3004. This laser pulse partition/sampling process is shownwith continuous instant/momentary power, P, and discrete, momentary-mean(M2)-power, P. Here sampling 3005 is performed such that areas 3006 and3007 are equal. (This procedure is similar to Riemann-limit integration,for mathematical integrals.) M2-power, power values, P, are thosemeasured by photodetector gating process, with photodetector pixelbandwidth, B, where

$\begin{matrix}{{B = \frac{1}{\left( {\delta\; t} \right)_{B}}};{\left( {\delta\; t} \right)_{B} < \left( {\delta\; t} \right)_{L}}} & (110)\end{matrix}$where (δt)_(L) is laser pulse temporal length, previously denoted as(δt). Of course, when (δt)_(B)→0 (or, B→∞), then, the discrete M2-powerline 3003, becomes continuous (analog) line 3002.

It should be noted that the analog instant (optical) power line 3002 canbe only measured as discrete M2-power line 3003, while inequality (Eq.110) can be written as:

$\begin{matrix}{\left( {\delta\; t} \right)_{B} = \frac{\left( {\delta\; t} \right)_{L}}{m}} & (111)\end{matrix}$where m is integer: m=1, 2, 3, . . . . For example, for pulse length:(δt)_(L)=10 nsec=10⁻⁸ sec, and m=10, (δt)_(B)=1 nsec=10⁻⁹ sec, and,according to Eq. (77), B=1 GHz.

Such pulse sampling allows the system to measure reflected pulses, withhigher precision than, without sampling. For example, if soilpenetration depth is equal to:Δz=k(δz)_(B) ;k=1,2,3, . . .   (112)where (δt)_(B) is voxel resolving element, determined by relation:2(δz)_(B)=(C/n)(δt)_(B)  (113)where C is light speed in air, and n—soil refractive index; then,reflected pulse will be deformed, respectively.

Various targets may be detected according to their temporal signaturesof reflected pulse and related pulse partition voxel coherency (PPVC),which is a generalization of voxel coherency (VC). For sake ofexplanation rectangular pulse are illustrated instead of analog(Gaussian) pulse. Then, the reflected pulse from hard interface, as inFIG. 31A, will be (almost) un-deformed, 3100, while pulse reflected alsofrom soft interface, 3101 as in FIG. 31B, will have tail, 3102. In FIG.31C, the reflection from partially-transparent two hard interfaces isshown, with incident pulse, 3103, marked by left-to right arrow, 3104,is shown, including reflected pulse, 3105, marked by right-to-leftarrow, 3106. 2^(nd) reflected pulse, 3107, is lower than the 1^(st)reflected pulse, 3108, with separation, Δz, denoted as 3109, and itsequivalent temporal separation, equal to: (2Δz·n)/c, marked as 3110. InFIG. 31D, the reflected pulse signature 3111, is shown, versus incidentpulse, 3112, out of scale, for closer separation, 3113. Then, thereflected pulse signature has an extra top addition, 3113, assumingincoherent superposition (beam intensities, not amplitudes, are added).In FIG. 31E, the reflection from two hard interfaces, 3114 and 3115, isshown, with attenuation in region 3116, without reflection from softinterface, however. This is, because we assume that there is noreflection/scattering centers, in region 3116. In contrast, in FIG. 31F,such centers exit in soft interface region, 3117. As a result, inaddition to two strong reflection signatures, 3118 and 3119, we havealso weak reflection tail, 3120.

As used herein, the term module might describe a given unit offunctionality that can be performed in accordance with one or moreembodiments of the present invention. As used herein, a module might beimplemented utilizing any form of hardware, software, or a combinationthereof. For example, one or more processors, controllers, ASICs, PLAs,PALs, CPLDs, FPGAs, logical components, software routines or othermechanisms might be implemented to make up a module. In implementation,the various modules described herein might be implemented as discretemodules or the functions and features described can be shared in part orin total among one or more modules. In other words, as would be apparentto one of ordinary skill in the art after reading this description, thevarious features and functionality described herein may be implementedin any given application and can be implemented in one or more separateor shared modules in various combinations and permutations. Even thoughvarious features or elements of functionality may be individuallydescribed or claimed as separate modules, one of ordinary skill in theart will understand that these features and functionality can be sharedamong one or more common software and hardware elements, and suchdescription shall not require or imply that separate hardware orsoftware components are used to implement such features orfunctionality.

Where components or modules of the invention are implemented in whole orin part using software, in one embodiment, these software elements canbe implemented to operate with a computing or processing module capableof carrying out the functionality described with respect thereto. Onesuch example computing module is shown in FIG. 32. Various embodimentsare described in terms of this example-computing module 3200. Afterreading this description, it will become apparent to a person skilled inthe relevant art how to implement the invention using other computingmodules or architectures.

Referring now to FIG. 32, computing module 3200 may represent, forexample, computing or processing capabilities found within desktop,laptop and notebook computers; hand-held computing devices (PDA's, smartphones, cell phones, palmtops, etc.); mainframes, supercomputers,workstations or servers; or any other type of special-purpose orgeneral-purpose computing devices as may be desirable or appropriate fora given application or environment. Computing module 3200 might alsorepresent computing capabilities embedded within or otherwise availableto a given device. For example, a computing module might be found inother electronic devices such as, for example, digital cameras,navigation systems, cellular telephones, portable computing devices,modems, routers, WAPs, terminals and other electronic devices that mightinclude some form of processing capability.

Computing module 3200 might include, for example, one or moreprocessors, controllers, control modules, or other processing devices,such as a processor 3204. Processor 3204 might be implemented using ageneral-purpose or special-purpose processing engine such as, forexample, a microprocessor, controller, or other control logic. In theillustrated example, processor 3204 is connected to a bus 3202, althoughany communication medium can be used to facilitate interaction withother components of computing module 3200 or to communicate externally.

Computing module 3200 might also include one or more memory modules,simply referred to herein as main memory 3208. For example, preferablyrandom access memory (RAM) or other dynamic memory, might be used forstoring information and instructions to be executed by processor 3204.Main memory 3208 might also be used for storing temporary variables orother intermediate information during execution of instructions to beexecuted by processor 3204. Computing module 3200 might likewise includea read only memory (“ROM”) or other static storage device coupled to bus3202 for storing static information and instructions for processor 3204.

The computing module 3200 might also include one or more various formsof information storage mechanism 3210, which might include, for example,a media drive 3212 and a storage unit interface 3220. The media drive3212 might include a drive or other mechanism to support fixed orremovable storage media 3214. For example, a hard disk drive, a floppydisk drive, a magnetic tape drive, an optical disk drive, a CD or DVDdrive (R or RW), or other removable or fixed media drive might beprovided. Accordingly, storage media 3214 might include, for example, ahard disk, a floppy disk, magnetic tape, cartridge, optical disk, a CDor DVD, or other fixed or removable medium that is read by, written toor accessed by media drive 3212. As these examples illustrate, thestorage media 3214 can include a computer usable storage medium havingstored therein computer software or data.

In alternative embodiments, information storage mechanism 3210 mightinclude other similar instrumentalities for allowing computer programsor other instructions or data to be loaded into computing module 3200.Such instrumentalities might include, for example, a fixed or removablestorage unit 3222 and an interface 3220. Examples of such storage units3222 and interfaces 3220 can include a program cartridge and cartridgeinterface, a removable memory (for example, a flash memory or otherremovable memory module) and memory slot, a PCMCIA slot and card, andother fixed or removable storage units 3222 and interfaces 3220 thatallow software and data to be transferred from the storage unit 3222 tocomputing module 3200.

Computing module 3200 might also include a communications interface3224. Communications interface 3224 might be used to allow software anddata to be transferred between computing module 3200 and externaldevices. Examples of communications interface 3224 might include a modemor softmodem, a network interface (such as an Ethernet, networkinterface card, WiMedia, IEEE 802.XX or other interface), acommunications port (such as for example, a USB port, IR port, RS232port Bluetooth® interface, or other port), or other communicationsinterface. Software and data transferred via communications interface3224 might typically be carried on signals, which can be electronic,electromagnetic (which includes optical) or other signals capable ofbeing exchanged by a given communications interface 3224. These signalsmight be provided to communications interface 3224 via a channel 3228.This channel 3228 might carry signals and might be implemented using awired or wireless communication medium. Some examples of a channel mightinclude a phone line, a cellular link, an RF link, an optical link, anetwork interface, a local or wide area network, and other wired orwireless communications channels.

In this document, the terms “computer program medium” and “computerusable medium” are used to generally refer to media such as, forexample, memory 3208, storage unit 3220, media 3214, and channel 3228.These and other various forms of computer program media or computerusable media may be involved in carrying one or more sequences of one ormore instructions to a processing device for execution. Suchinstructions embodied on the medium, are generally referred to as“computer program code” or a “computer program product” (which may begrouped in the form of computer programs or other groupings). Whenexecuted, such instructions might enable the computing module 3200 toperform features or functions of the present invention as discussedherein.

While various embodiments of the present invention have been describedabove, it should be understood that they have been presented by way ofexample only, and not of limitation. Likewise, the various diagrams maydepict an example architectural or other configuration for theinvention, which is done to aid in understanding the features andfunctionality that can be included in the invention. The invention isnot restricted to the illustrated example architectures orconfigurations, but the desired features can be implemented using avariety of alternative architectures and configurations. Indeed, it willbe apparent to one of skill in the art how alternative functional,logical or physical partitioning and configurations can be implementedto implement the desired features of the present invention. Also, amultitude of different constituent module names other than thosedepicted herein can be applied to the various partitions. Additionally,with regard to flow diagrams, operational descriptions and methodclaims, the order in which the steps are presented herein shall notmandate that various embodiments be implemented to perform the recitedfunctionality in the same order unless the context dictates otherwise.

Although the invention is described above in terms of various exemplaryembodiments and implementations, it should be understood that thevarious features, aspects and functionality described in one or more ofthe individual embodiments are not limited in their applicability to theparticular embodiment with which they are described, but instead can beapplied, alone or in various combinations, to one or more of the otherembodiments of the invention, whether or not such embodiments aredescribed and whether or not such features are presented as being a partof a described embodiment. Thus, the breadth and scope of the presentinvention should not be limited by any of the above-described exemplaryembodiments.

Terms and phrases used in this document, and variations thereof, unlessotherwise expressly stated, should be construed as open ended as opposedto limiting. As examples of the foregoing: the term “including” shouldbe read as meaning “including, without limitation” or the like; the term“example” is used to provide exemplary instances of the item indiscussion, not an exhaustive or limiting list thereof; the terms “a” or“an” should be read as meaning “at least one,” “one or more” or thelike; and adjectives such as “conventional,” “traditional,” “normal,”“standard,” “known” and terms of similar meaning should not be construedas limiting the item described to a given time period or to an itemavailable as of a given time, but instead should be read to encompassconventional, traditional, normal, or standard technologies that may beavailable or known now or at any time in the future. Likewise, wherethis document refers to technologies that would be apparent or known toone of ordinary skill in the art, such technologies encompass thoseapparent or known to the skilled artisan now or at any time in thefuture.

The presence of broadening words and phrases such as “one or more,” “atleast,” “but not limited to” or other like phrases in some instancesshall not be read to mean that the narrower case is intended or requiredin instances where such broadening phrases may be absent. The use of theterm “module” does not imply that the components or functionalitydescribed or claimed as part of the module are all configured in acommon package. Indeed, any or all of the various components of amodule, whether control logic or other components, can be combined in asingle package or separately maintained and can further be distributedin multiple groupings or packages or across multiple locations.

Additionally, the various embodiments set forth herein are described interms of exemplary block diagrams, flow charts and other illustrations.As will become apparent to one of ordinary skill in the art afterreading this document, the illustrated embodiments and their variousalternatives can be implemented without confinement to the illustratedexamples. For example, block diagrams and their accompanying descriptionshould not be construed as mandating a particular architecture orconfiguration.

The invention claimed is:
 1. A target detection system, comprising: alaser light emitter configured to emit a laser flash comprising at leastone diverging laser pulse having a pulse length emitted at a pulsefrequency, the laser flash sufficient to illuminate a detection volumeat a distance from the light emitter and; a pseudoimaging opticalreceiver system configured to receive the laser flash after reflectionfrom objects in the detection volume and to transmit reflected lightreturning from the detection volume to a photodetector array, theoptical receiver system having a circle of confusion larger than adistance between adjacent photodetectors of the photodetector array; andthe photodetector array configured to provide a flash voxel readoutcomprising a series of time-gated energy readouts.
 2. The targetdetection system of claim 1, wherein the laser pulse has a wavelengthgreater than 1.0 μm.
 3. The target detection system of claim 1, furthercomprising a voxel processing module coupled to the readout moduleconfigured to detect a reference clutter signal in the series oftime-gated energy readouts and to locate a potential target signalrelative to the reference clutter signal.
 4. The target detection systemof claim 3, further comprising: a laser light source; and a normalizercoupled to the laser light source and the laser emitter.
 5. The targetdetection system of claim 4, wherein the normalizer comprises ashuffling fiber bundle.
 6. The target detection system of claim 5,wherein the normalizer further comprises an expanded beam couplercoupled to the laser light source and an input of the shuffling fiberbundle.
 7. The target detection system of claim 6, further comprising amultimode fiber connecting the laser light source to the expanded beamcoupler.
 8. The target detection system of claim 7, wherein themultimode fiber has a core diameter greater than or equal to 300 μm. 9.The target detection system of claim 3, wherein the pseudoimagingoptical receiver system comprises a filter passing the laser wavelength.10. The target detection system of claim 9, wherein the filter comprisesan interference passband filter having a center interference wavelengthunder normal incidence equal to the laser wavelength.
 11. The targetdetection system of claim 3, further comprising a mechanical trackingsystem coupled to the laser light emitter and adapted to rotate thelaser light emitter; and wherein the laser light emitter is configuredto emit a laser flash at a plurality of rotational locations.
 12. Thetarget detection system of claim 3, wherein the energy readouts arebinary readings, the binary readings having a first value if thephotodetector providing the reading detects less than a threshold amountof energy and having a second value if the photodetector providing thereading detects greater than or equal to the threshold amount of energy.13. The target detection system of claim 3, wherein the voxel processingmodule is configured to detect the potential target signal by detectinga missing reference clutter voxel in the reference clutter signal. 14.The target detection system of claim 13, wherein the voxel processingmodule is further configured to detect the potential target signal bydetecting a voxel with energy corresponding to the missing referenceclutter voxel.
 15. The target detection system of claim 14, wherein thevoxel processing module is further configured to detect the potentialtarget signal by determining the distance between the voxel with energycorresponding to the missing reference clutter voxel and the missingreference clutter volume.
 16. The target detection system of claim 15,wherein the voxel processing module is further configured to detect thepotential target signal if the distance is greater than a distancethreshold.
 17. The target detection system of claim 13, wherein: thereference clutter signal comprises voxels corresponding to volumescontaining clutter; and the voxel processing module is furtherconfigured to detect the potential target signal by detecting aplurality of voxels with energy corresponding to a plurality of missingreference clutter voxels, the plurality of voxels with energy includingvoxels with energy that correspond to volumes closer than volumescontaining clutter and including voxels with energy that correspond tovolumes farther than volumes containing clutter.
 18. The targetdetection system of claim 3, wherein the pseudoimaging optical receiversystem comprises a tapered fiber array, the tapered fiber array having aseparate output for each photodetector of the photodetector array. 19.The target detection system of claim 3, wherein the laser light emitterand pseudoimaging optical receiver are mounted on a platform; andfurther comprising a stabilizer coupled to the platform and configuredto stabilize the platform from the beginning of the laser flash untilthe laser flash has been received by the pseudoimaging optical receiversystem.
 20. The target detection system of claim 3, further comprising apolarizer coupled to the laser light emitter configured to polarize thelaser flash.
 21. The target detection system of claim 20, furthercomprising a polarization detector array coupled to the voxel processingmodule and configured to detect the polarization of the reflected lightincident on each photodetector of the photodetector array to generate aflash polarization readout comprising a series of time-gatedpolarization readouts corresponding to the series of time-gated energyreadouts and configured to provide the flash polarization readout to thevoxel processing module.
 22. The target detection system of claim 20,further comprising a polarized filter coupled to the optical receiversystem and adapted to pass light having a polarization equal to thepolarization of the laser flash.
 23. The target detection system ofclaim 3, wherein the series of time-gated energy readouts is determinedby sampling the photodetector array multiple times during each pulse.24. The target detection system of claim 23, wherein the voxelprocessing module is configured to use the multiple samples during eachpulse to determine a reflected pulse shape of the potential targetsignal.
 25. The target detection system of claim 24, wherein the voxelprocessing module is configured to evaluate the potential target signalaccording to the reflected pulse shape of potential target signal. 26.The target detection system of claim 3, wherein: the laser light emitteris configured to emit a plurality of laser flashes sufficient toilluminate the detection volume at a plurality of illumination times;and the photodetector array is configured to provide a plurality offlash readouts corresponding to the plurality of illumination times. 27.The target detection system of claim 3, wherein the photodetector arraycomprises a one-dimensional photodetector array or a two-dimensionalphotodetector array.
 28. The target detection system of claim 3, whereinthe potential target signal is a reflection from a marine target and thereference clutter signal comprises reflection signals from sea clutter.29. The target detection system of claim 3, wherein the potential targetsignal is a reflection from a ground target and the reference cluttersignal comprises reflection signals from ground clutter.
 30. The targetdetection system of claim 3, wherein the potential target signal is aomnipulse signal.
 31. The target detection system of claim 1, whereinthe pseudoimaging optical receiver system comprises a compound lenssystem.
 32. The target detection system of claim 31, wherein thecompound lens system comprises a compound parabolic concentrator. 33.The target detection system of claim 1, wherein the emitter is disposedon a mast, an airborne platform, or a ground platform.
 34. The targetdetection system of claim 1, wherein the distance from the light emitteris determined according to a visibility condition.
 35. The system ofclaim 1, further comprising a second pseudoimaging optical receiversystem.
 36. The system of claim 1, wherein the second pseudoimagingoptical receiver system is configured to receive a second laser flashemitted by a second laser light emitter.
 37. A method, comprising:emitting a laser flash comprising at least one diverging laser pulsehaving a pulse length emitted at a pulse frequency, the laser flashsufficient to illuminate a detection volume located at least 3 km from alaser light emitter; receiving the laser flash at a pseudoimagingoptical receiver after reflection from objects in the detection volumeand transmitting reflected light returning from the detection volume toa photodetector array, the optical receiver system having a circle ofconfusion larger than a distance between adjacent photodetectors of thephotodetector array; obtaining a flash voxel readout from thepseudoimaging optical receiver; detecting a reference clutter signal inthe series of time-gated energy readouts; and locating a potentialtarget signal relative to the reference clutter signal.
 38. The methodof claim 37, wherein the energy readouts are binary readings, the binaryreadings having a first value if the photodetector providing the readingdetects less than a threshold amount of energy and having a second valueif the photodetector providing the reading detects greater than or equalto the threshold amount of energy.
 39. The method of claim 37, furthercomprising detecting the potential target signal by detecting a missingreference clutter voxel in the reference clutter signal.
 40. The methodof claim 37, further comprising detecting the potential target signal bydetermining the distance between the voxel with energy corresponding tothe missing reference clutter voxel and the missing reference cluttervolume.
 41. The method of claim 37, further comprising detecting thepotential target signal if the distance is greater than a distancethreshold.
 42. The method of claim 37, wherein the reference cluttersignal comprises voxels corresponding to volumes containing clutter; andfurther comprising detecting the potential target signal by detecting aplurality of voxels with energy corresponding to a plurality of missingreference clutter voxels, the plurality of voxels with energy includingvoxels with energy that correspond to volumes closer than volumescontaining clutter and including voxels with energy that correspond tovolumes farther than volumes containing clutter.
 43. The method of claim37, further comprising, distinguishing between a first plurality ofpotential targets by detecting which of the first plurality of potentialtargets are retroreflectors.
 44. The method of claim 43, furthercomprising, distinguishing between a second plurality of potentialtargets by detecting omnipulse signatures.
 45. The method of claim 44,wherein the second plurality of potential targets are theretroreflectors of the first plurality of potential targets.
 46. Themethod of claim 37, wherein the laser pulse has a laser wavelengthgreater than 1.0 μm.